1. Two different quadratic equations have a common root. Let the three unique roots of the two equations be A, B and C - all of them are positive integers. If (A + B + C) = 41 and the product of the roots of one of the equations is 35, which of the following options is definitely correct?
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By: anil on 05 May 2019 02.34 am
It has been given that A+B+C = 41.
Let the common root be B.
All the roots are positive integers.
The product of the roots of one of the equations is 35.
35 can be obtained only in 2 ways - either as 5*7 or 35*1.
A+B+C = 41.
If A and B are 5 and 7 in any order, then C = 41 - 5 - 7 = 29.
If A and B are 35 and 1 in any order, then C = 41 - 35 - 1 = 5.
As we can see, in either case, 5 is one of the 3 roots.
Therefore, option C is the right answer.
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Let the common root be B.
All the roots are positive integers.
The product of the roots of one of the equations is 35.
35 can be obtained only in 2 ways - either as 5*7 or 35*1.
A+B+C = 41.
If A and B are 5 and 7 in any order, then C = 41 - 5 - 7 = 29.
If A and B are 35 and 1 in any order, then C = 41 - 35 - 1 = 5.
As we can see, in either case, 5 is one of the 3 roots.
Therefore, option C is the right answer.