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CAT 2001 — QA Question 44

Forming a Quadratic Equation and Relation between roots and coefficientsEasy
Passage / Data

Answer the following question based on the information given below.

The batting average (BA) of a test batsman is computed from runs scored and innings played-completed innings and incomplete innings (not out) in the following manner:

r1 = number of runs scored in completed innings; n1 = number of completed innings

r2 = number of runs scored in incomplete innings; n2 = number of incomplete innings

BA = r1+r2n1

To better assess batsman's accomplishments, the ICC is considering two other measures MBA1 and MBA2 defined as follows:

MBA1 = r1n1+n2n1× max[0, (r2n2-r1n1])

MBA2 = r1+r2n1+n2

Ujakar and Keshab attempted to solve a quadratic equation. Ujakar made a mistake in writing down the constant term. He ended up with the roots (4, 3). Keshab made a mistake in writing down the coefficient of x. He got the root as (3, 2). What will be the exact roots of the original quadratic equation?

Answer & solution

  • (6, 1)

  • B

    (–3, –4)

  • C

    (4, 3)

  • D

    (–4, –3)

Solution

In Ujakar’s case, the constant term is wrong.

∴ Product of roots will be wrong but the sum of roots will be correct.

∴ Correct Sum of the roots = 4 + 3 = 7

In Keshab’s case, coefficient of x is wrong.

∴ Sum of roots will be wrong but the product of roots will be correct.

∴ Correct product of roots = 3 × 2 = 6

∴ Correct quadratic equation is x2 – 7x + 6 = 0

(x – 6)(x – 1) = 0

∴ x = 6 or x = 1

Hence, option (a).

CAT 2001 QA Q44: Ujakar and Keshab attempted to solve a quadratic equation. Ujakar made a mistake in writing down the constant — Solution | TheCATExam