If the equation $$x^3 - ax^2 + bx - a = 0$$ has three real roots, then it must be the case that, ?->(Show Answer!)

1. If the equation $$x^3 - ax^2 + bx - a = 0$$ has three real roots, then it must be the case that,

Write Comment

Comments

By: anil on 05 May 2019 02.31 am

It can be clearly seen that if b=1 then $$x^2(x - a) + (x - a) = 0$$ an the equation gives only 1 real value of x

Tags

Show Similar Question And Answers

QA->If the solution set of the equation ax2+bx+c=0 is {α, β} then α-β is:....

QA->The characteristic equation of gas is :....

QA->Real Madrid midfielder who has been named 2014 Sportsman of the Year by the AIPS (International Association of Latin American Sports Journalists) for his performances with Colombia in the 2014 World Cup and with Real Madrid?....

QA->The prime accused in the multi-crore fake stamp paper case, who has been sentenced to seven years of rigorous imprisonment in a 2001 case by a special court on September 18, 2010?....

QA->A cyclist goes 40 km towards East and then turning to right he goes 40 km. Again he turn to his left and goes 20 km. After this he turns to his left and goes 40 km, then again turns right and goes 10km. How far is he from his starting point?....

MCQ-> Read the following passage carefully and answer the questions given at the end. When Ratan Tata moved the Supreme Court, claiming his right to privacy had been violated, he called Harish Salve. The choice was not surprising. The former solicitor general had been topping the legal charts ever since he scripted a surprising win for Mukesh Ambani against his brother Anil. That dispute set the gold standard for legal fees. On Mukesh’s side were Salve, Rohinton Nariman, and Abhishek Manu Singhvi. The younger brother had an equally formidable line-up led by Ram Jethmalani and Mukul Rohatgi.The dispute dated back three-and-a-half years to when Anil filed case against his brother for reneging on an agreement to supply 28 million cubic metres of gas per day from its Krishna-Godavari basin fields at a rate of $ 2.34 for 17 years. The average legal fee was Rs. 25 lakh for a full day's appearance, not to mention the overnight stays at Mumbai's five-star suites, business class travel, and on occasion, use of the private jet. Little wonder though that Salve agreed to take on Tata’s case pro bono. He could afford philanthropy with one of India’s wealthiest tycoons.The lawyers’ fees alone, at a conservative estimate, must have cost the Ambanis at least Rs. 15 crore each. Both the brothers had booked their legal teams in the same hotel, first the Oberoi and, after the 26/ ll Mumbai attacks, the Trident. lt’s not the essentials as much as the frills that raise eyebrows. The veteran Jethmalani is surprisingly the most modest in his fees since he does not charge rates according to the strength of the client's purse. But as the crises have multiplied, lawyers‘fees have exploded.The 50 court hearings in the Haldia Petrochemicals vs. the West Bengal Government cost the former a total of Rs. 25 crore in lawyer fees and the 20 hearings in the Bombay Mill Case, which dragged on for three years, cost the mill owners almost Rs. 10 crore. Large corporate firms, which engage star counsels on behalf of the client, also need to know their quirks. For instance, Salve will only accept the first brief. He will never be the second counsel in a case. Some lawyers prefer to be paid partly in cash but the best are content with cheques. Some expect the client not to blink while picking up a dinner tab of Rs. 1.75 lakh at a Chennai five star. A lawyer is known to carry his home linen and curtains with him while travelling on work. A firm may even have to pick up a hot Vertu phone of the moment or a Jaeger-LeCoutre watch of the hour to keep a lawyer in good humour.Some are even paid to not appear at all for the other side - Aryama Sundaram was retained by Anil Ambani in the gas feud but he did not fight the case. Or take Raytheon when it was fighting the Jindals. Raytheon had paid seven top lawyers a retainer fee of Rs. 2.5 lakh each just to ensure that the Jindals would not be able to make a proper case on a taxation issue. They miscalculated when a star lawyer fought the case at the last minute. “I don’t take negative retainers”, shrugs Rohatgi, former additional solicitor general. “A Lawyer’s job is to appear for any client that comes to him. lt’s not for the lawyers to judge if a client is good or bad but the court”. Indeed. He is, after all, the lawyer who argued so famously in court that B. Ramalinga Raju did not ‘fudge any account in the Satyam Case. All he did was “window dressing”.Some high profile cases have continued for years, providing a steady source of income, from the Scindia succession battle which dates to 1989, to the JetLite Sahara battle now in taxation arbitration to the BCCI which is currently in litigation with Lalit Modi, Rajasthan Royals and Kings XI Punjab.Think of the large law firms as the big Hollywood studios and the senior counsel as the superstar. There are a few familiar faces to be found in most of the big ticket cases, whether it is the Ambani gas case, Vodafone taxation or Bombay Mills case. Explains Salve, “There is a reason why we have more than one senior advocate on a case. When you're arguing, he’s reading the court. He picks up a point or a vibe that you may have missed.” Says Rajan Karanjawala, whose firm has prepared the briefs for cases ranging from the Tata's recent right to privacy case to Karisma Kapoor’s divorce, “The four jewels in the crown today are Salve, Rohatgi, Rohinton Nariman and Singhvi. They have replaced the old guard of Fali Nariman, Soli Sorabjee, Ashok Desai and K.K. Venugopal.” He adds, “The one person who defies the generational gap is Jethmalani who was India's leading criminal lawyer in the 1960s and is so today.”The demand for superstar lawyers has far outstripped the supply. So a one-man show by, say, Rohatgi can run up billings of Rs. 40 crore, the same as a mid-sized corporate law firm like Titus and Co that employs 28 juniors. The big law filik such as AZB or Amarchand & Mangaldas or Luthra & Luthra have to do all the groundwork for the counsel, from humouring the clerk to ensure the A-lister turns up on the hearing day to sourcing appropriate foreign judgments in emerging areas such as environmental and patent laws. “We are partners in this. There are so few lawyers and so many matters,” points out Diljeet Titus.As the trust between individuals has broken down, governments have questioned corporates and corporates are questioning each other, and an array of new issues has come up. The courts have become stronger. “The lawyer,” says Sundaram, with the flourish that has seen him pick up many Dhurandhares and Senakas at pricey art auctions, “has emerged as the modern day purohit.” Each purohit is head priest of a particular style. Says Karanjawala, “Harish is the closest example in today's bar to Fali Nariman; Rohinton has the best law library in his brain; Mukul is easily India's busiest lawyer while Manu Singhvi is the greatest multi-tasker.” Salve has managed a fine balancing act where he has represented Mulayam Singh Yadav and Mayawati, Parkash Singh Badal and Amarinder Singh, Lalit Modi and Subhash Chandra and even the Ambani brothers, of course in different cases. Jethmalani is the man to call for anyone in trouble. In judicial circles he is known as the first resort for the last resort. Even Jethmalani’s junior Satish Maneshinde, who came to Mumbai in I993 as a penniless law graduate from Karnataka, shot to fame (and wealth) after he got bail for Sanjay Dutt in 1996. Now he owns a plush office in Worli and has become a one-stop shop for celebrities in trouble.Which of the following is not true about Ram Jethmalani?
....

MCQ->What will be the output of the C#.NET code snippet given below? char ch = Convert.ToChar ('a' | 'b' | 'c'); switch (ch) { case 'A': case 'a': Console.WriteLine ("case A | case a"); break; case 'B': case 'b': Console.WriteLine ("case B | case b"); break; case 'C': case 'c': case 'D': case 'd': Console.WriteLine ("case D | case d"); break; }....

MCQ->Consider the following statements: If any root of characteristic equation has a positive real part the impulse response is unbounded and system is unstable.If all the roots of a characteristic equation have negative real parts, the impulse response decays to zero.If one or more non-repeated roots of characteristic equation are on jω axis impulse response is bounded but the system is unstable. Which of the above equations are correct?....

MCQ-> Read the passage given below and answer the questions that follow:-Brazil is a top exporter of every commodity that has seen dizzying price surges - iron ore, soybeans, sugar - producing a golden age for economic growth Foreign money-flows into Brazilian stocks and bonds climbed heavenward, up more than tenfold, from $5 billion a year in early 2007 to more than $50 billion in the twelve months through March 2011.The flood of foreign money buying up Brazilian assets has made the currency one of the most expensive in the world, and Brazil one of the most costly, overhyped economies. Almost every major emerging- market currency has strengthened against the dollar over the last decade, but the Brazilian Real is on a path alone, way above the pack, having doubled in value against the dollar.Economists have all kinds of fancy ways to measure the real value of a currency, but when a country is pricing itself this far out of the competition, you can feel it on the ground. In early 2011 the major Rio paper, 0 Globo, ran a story on prices showing that croissants are more expensive than they are in Paris, haircuts cost more than they do in London, bike rentals are more expensive than in Amsterdam, and movie tickets sell for higher prices than in Madrid. A rule of the road: if the local prices in an emerging market country feel expensive even to a visitor from a rich nation, that country is probably not a breakout nation.There is no better example of how absurd it is to lump all the big emerging markets together than the frequent pairing of Brazil and China. Those who make this comparison are referring only to the fact that they are the biggest players in their home regions, not to the way the economies actually run. Brazil is the world‘s leading exporter of many raw materials, and China is the leading importer; that makes them major trade partners - China surpassed the United States as Brazil's leading trade partner in 2009 f but it also makes them opposites in almost every important economic respect: Brazil is the un-China, with interest rates that are too high, and a currency that is too expensive. It spends too little on roads and too much on welfare, and as a result has a very un-China-like growth record.It may not be entirely fair to compare economic growth in Brazil with that of its Asian counterparts, because Brazil has a per capita income of $12,000, more than two times China's and nearly ten times India's. But even taking into account the fact that it is harder for rich nations to grow quickly, Brazil's growth has been disappointing. Since the early 19805 the Brazilian growth rate has oscillated around an average of 2.5 percent, spiking only in concert with increased prices for Brazil's key commodity exports. While China has been criticized for pursuing "growth at any cost," Brazil has sought to secure "stability at any cost." Brazil's caution stems from its history of financial crises, in which overspending produced debt, humiliating defaults, and embarrassing devaluations, culminating in a disaster that is still recent enough to be fresh in every Brazilian adult's memory: the hyperinflation that started in the early 19805 and peaked in 1994, at the vertiginous annual rate of 2,100 percent.Wages were pegged to inflation but were increased at varying intervals in different industries, 50 workers never really knew whether they were making good money or not. As soon as they were paid, they literally ran to the store with cash to buy food, and they could afford little else, causing non-essential industries to start to die. Hyperinflation finally came under control in l995, but it left a problem of regular behind. Brazil has battled inflation ever since by maintaining one of the highest interest rates in the emerging world. Those high rates have attracted a surge of foreign money, which is partly why the Brazilian Real is so expensive relative to comparable currencies.There is a growing recognition that China faces serious "imbalances" that could derail its long economic boom. Obsessed until recently with high growth, China has been pushing too hard to keep its currency too cheap (to help its export industries compete), encouraging excessively high savings and keeping interest rates rock bottom to fund heavy spending on roads and ports. China is only now beginning to consider a shift in spending priorities to create social programs that protect its people from the vicissitudes of old age and unemployment.Brazil’s economy is just as badly out of balance, though in opposite ways. While China has introduced reforms relentlessly for three decades, opening itself up to the world even at the risk of domestic instability, Brazil has pushed reforms only in the most dire circumstances, for example, privatizing state companies when the government budget is near collapse. Fearful of foreign shocks, Brazil is still one of the most closed economies in the emerging world - total imports and exports account for only 15 percent of GDP - despite its status as the world's leading exporter of sugar, orange juice, coffee, poultry, and beef.To pay for its big government, Brazil has jacked up taxes and now has a tax burden that equals 38 percent of GDP, the highest in the emerging world, and very similar to the tax burden in developed European welfare states, such as Norway and France. This heavy load of personal and corporate tax on a relatively poor country means that businesses don’t have the money to invest in new technology or training, which in turn means that industry is not getting more efficient. Between 1986 and 2008 Brazil’s productivity grew at an annual rate of :about 0.2 percent, compared to 4 percent in China. Over the same period, productivity grew in India at close to 3 percent and in South Korea and Thailand at close to 2 percent. According to the passage, the major concern facing the Brazil economy is:
....