A student attempted to solve a quadratic equation in x twice. However, in the first attempt, he incorrectly wrote the constant term and ended up with the roots as (4, 3). In the second attempt, he incorrectly wrote down the coefficient of x and got the roots as (3, 2). Based on the above information, the roots of the correct quadratic equation are A. (-3, 4) B. (3, -4) C. (6, 1) D. (4, 2)

GATE 2011 · General Aptitude · Quadratic Equations · medium

Answer: The roots of the correct quadratic equation are 6 and 1.

1. Extract correct sum of roots: First attempt gives roots 4 and 3 with correct coefficient of x. Sum = 4 + 3 = 7. So correct sum of roots = 7.
2. Extract correct product of roots: Second attempt gives roots 3 and 2 with correct constant term. Product = 3 * 2 = 6. So correct product of roots = 6.
3. Form and solve the correct quadratic: Correct equation: x^2 - 7x + 6 = 0. Factoring: (x - 6)(x - 1) = 0. Roots = 6, 1.