CAT 2001 — QA Question 44
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
Correct answer: (6, 1)
(6, 1)
- B
(–3, –4)
- C
(4, 3)
- D
(–4, –3)
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).