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For a quadratic equation with roots x and y the sum and the product of the roots is 7 and 6 respectively. What is the sum of the roots of the quadratic equation having positive integer roots, and whose product of roots is given by x2(1 - y) + 2xy + y2( 1 - x)?
  • a)
    1
  • b)
    7
  • c)
    8
  • d)
    9
  • e)
    Cannot be determined
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
For a quadratic equation with roots x and y the sum and the product of...
x + y =7 and xy = 6
x2(1 - y) + 2xy + y2 (1 - x) = x2 + 2xy + y2 - x2y - xy2 = (x + y)(x + y -xy ) = 7(7-6) = 7
Since the two roots are positive integers, product of the roots can be 7 only when the roots are 1 and 7.
Sum of roots = 1 + 7 = 8
Hence, option 3.
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For a quadratic equation with roots x and y the sum and the product of the roots is 7 and 6 respectively. What is the sum of the roots of the quadratic equation having positive integer roots, and whose product of roots is given by x2(1 - y) + 2xy + y2( 1 - x)?a)1b)7c)8d)9e)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?
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