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XAT 2018 — QA & DI Question 10

Two Quadratic EquationsEasy

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?

Answer & solution

  • A

    The common root is 29. 

  • B

    The smallest among the roots is 1. 

  • One of the roots is 5. 

  • D

    Product of the roots of the other equation is 5. 

  • E

    All of the above are possible, but none are definitely correct.

Solution

A, B and C are positive integers.

Let the common root is A.

∴ A × B = 35

This is possible when (A, B) is (1, 35) or (35, 1) or (5, 7) or (7, 5)

C = 41 – A - B

For each of these 4 possibilities value of C = 5 or 5 or 29 or 29

In each of these 4 possibilities, one of the roots is definitely 5.

Hence, option (c).

XAT 2018 QA & DI Q10: Two different quadratic equations have a common root. Let the three unique roots of the two equations be A, B — Solution | TheCATExam