If the expression $$px^3 - qx^2 - 7x - 6$$ is completely divisible by $$x^2 - x - 6$$, then what is the value of p and q respectively? ?->(Show Answer!)

1. If the expression $$px^3 - qx^2 - 7x - 6$$ is completely divisible by $$x^2 - x - 6$$, then what is the value of p and q respectively?

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By: anil on 05 May 2019 01.47 am

Expression : $$f(x)px^3 - qx^2 - 7x - 6$$ is divisible by $$x^2 - x - 6$$ => $$x^2-x-6=0$$ => $$(x-3)(x+2)=0$$ => $$x=3,-2$$ Thus, $$f(3)=0$$ => $$p(3)^3-q(3)^2-7(3)-6=0$$ => $$27p-9q-21-6=0$$ => $$27p-9q=27$$ => $$3p-q=3$$ -----------(i) Also, $$f(-2)=0$$ => $$p(-2)^3-q(-2)^2-7(-2)-6=0$$ => $$-8p-4q+14-6=0$$ => $$8p+4q=8$$ => $$2p+q=2$$ -----------(ii) Adding equations (i) and (ii), => $$5p=3+2=5$$ => $$p=1$$ Substituting it in equation (ii), => $$q=2-2(1)=0$$ => Ans - (B)

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MCQ-> Read the following passage carefully and answer the questions given below it. Certain words/phrases have been printed in bold to help you locate them while answering some of the questions. Once upon a time there was a King of Benaras who was very rich. He had many servants and a beautiful palace with wonderful gardens; he had chariots and a stable full of horses. But his most prized possession was a magnificent elephant called Mahaghiri. She was as tall as two men, and her skin was of the colour of thunder clouds. She had large flapping ears and small, bright eyes and she was very clever. Mahaghiri lived in her own special elephant house and had her own keeper, Rajinder. The King would often visit Mahaghiri to take her some special tit-bit to eat and check that Rajinder was looking after her properly. But Rajinder needed no reminding, for he also loved the elephant dearly, and trusted her completely. Every morning, he would take her down to the river for her bath. 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Spare no expense in finding a cure.” So the chief minister went to see Mahaghiri. who was still bound firmly with ropes. First he looked at her eyes – they were as clear and bright as usual. Then he felt behind her ears – her temperature was normal. Next he listened to her heart that was fine too – and checked all over for cuts or sores. He could find nothing wrong with her. “Strange,” he thought. “I can find no explanation for her bad behaviour.”But then his eye was caught by something gleaming in the straw. It was a sharp, curved knife, like the ones used by robbers. Could there be a connection? That night, when everyone else had gone to bed, the chief minister returned to the elephant house. There, in the stall next to Mahaghiri’s, sat a band of robbers. “Tonight we’ll burgle the palace,” said the chief. “First, we’ll make a hole in the wall, then we’ll steal the treasure. “But what about the guards?” someone asked. “Don’t tell me you’re still afraid to kill! When will you learn to be a real robber?” From the shadows, the minister could see the elephant, her ears pinned back, listening to every hateful and violent word.”Just as I suspected,” thought the minister. Then he slipped out, bolted the door on the outside so the robbers could not escape, and went immediately to the king.”Your majesty,” he said, “I think I have found the cause of your elephant’s bad behaviour.” As soon as the king heard what the minister had to say, he sent for his guards and had the robbers arrested. “But what about the elephant? 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A few years later, the tabla and, in the background, the pigeons and the itinerant kulfi seller, would inhabit a small graduate room in Oxford.cThe tape recorder, though, remains an extension of the oral transmission of music, rather than a replacement of it. And the oral transmission of North Indian classical music remains, almost uniquely, testament to the fact that the human brain can absorb, remember and reproduces structures of great complexity and sophistication without the help of the hieroglyph or written mark or a system of notation. I remember my surprise on discovering the Hazarilalji- who had mastered Kathak dance, tala and North Indian classical music, and who used to narrate to me, occasionally, compositions meant for dance that were grant and intricate in their verbal prosody, architecture and rhythmic complexity- was near illustrate and had barely learnt to write his name in large and clumsy letters.Of course, attempts have been made, throughout the 20th century, to formally codify and even notate this music, and institutions set up and degrees created, specifically to educate students in this “scientific” and codified manner. Paradoxically, however, this style of teaching has produced no noteworthy student or performer; the most creative musicians still emerge from the guru-shishya relationship, their understanding of music developed by oral communication.The fact that North Indian classical music emanates from, and has evolved through, oral culture, means that this music has a significantly different aesthetic, aw that this aesthetic has a different politics, from that of Western classical music) A piece of music in the Western tradition, at least in its most characteristic and popular conception, originates in its composer, and the connection between the two, between composer and the piece of music, is relatively unambiguous precisely because the composer writes down, in notation, his composition, as a poet might write down and publish his poem. However far the printed sheet of notated music might travel thus from the composer, it still remains his property; and the notion of property remains at the heart of the Western conception of “genius”, which derives from the Latin gignere or ‘to beget’.The genius in Western classical music is, then, the originator, begetter and owner of his work the printed, notated sheet testifying to his authority over his product and his power, not only of expression or imagination, but of origination. The conductor is a custodian and guardian of this property. IS it an accident that Mandelstam, in his notebooks, compares — celebratorily—the conductor’s baton to a policeman’s, saying all the music of the orchestra lies mute within it, waiting for its first movement to release it into the auditorium?The raga — transmitted through oral means — is, in a sense, no one’s property; it is not easy to pin down its source, or to know exactly where its provenance or origin lies. Unlike the Western classical tradition, where the composer begets his piece, notates it and stamps it with his ownership and remains, in effect, larger than, or the father of, his work, in the North India classical tradition, the raga — unconfined to a single incarnation, composer or performer — remains necessarily greater than the artiste who invokes it.This leads to a very different politics of interpretation and valuation, to an aesthetic that privileges the evanescent moment of performance and invocation over the controlling authority of genius and the permanent record. It is a tradition, thus, that would appear to value the performer, as medium, more highly than the composer who presumes to originate what, effectively, cannot be originated in a single person — because the raga is the inheritance of a culture.The author’s contention that the notion of property lies at the heart of the Western conception of genius is best indicated by which one of the following?
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