Multiple choice

Amit and Alok attempted to solve a quadratic equation. Amit made a mistake in writing down the constant term and ended up with roots (4, 3). Alok made a mistake in writing down coefficient of x to get roots (3, 2). The correct roots of the equation are:

  1. -4, -3

  2. 6, 1

  3. 4, 3

  4. -6, -1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Amit's roots (4,3) imply the equation is x^2 - 7x + k = 0. Alok's roots (3,2) imply x^2 - kx + 6 = 0. Comparing, the correct equation is x^2 - 7x + 6 = 0. Roots are 6 and 1.

AI explanation

Let the correct quadratic equation be x2 + bx + c = 0. Amit wrote the constant term incorrectly, but copied the coefficient of x correctly, so the sum of his roots (4, 3) gives the correct coefficient: 4 + 3 = -b, meaning b = -7. Alok wrote the coefficient of x incorrectly, but copied the constant term correctly, so the product of his roots (3, 2) gives the correct constant: 3 times 2 = 6, meaning c = 6. The correct equation is x2 - 7x + 6 = 0, which factors as (x - 6)(x - 1) = 0, yielding the correct roots 6 and 1.

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