Multiple choice

One of the two students, while solving a quadratic equation in x, copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of x2 correctly and got his roots as -6 and 1 respectively. The correct roots are

  1. 3, -2

  2. -3, 2
    • 6, -1

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

Let the equation be x^2 - Sx + P = 0. The first student got roots 3 and 2, so the sum S = 5 is correct, but the product P is wrong. The second student got roots -6 and 1, so the product P = -6 is correct, but the sum S = -5 is wrong. The correct equation is x^2 - 5x - 6 = 0. Factoring gives (x-6)(x+1) = 0, so roots are 6 and -1.

AI explanation

Let the correct quadratic equation be x2 + bx + c = 0. The first student copied the coefficient of x correctly but the constant term incorrectly, so using the incorrect roots of 3 and 2, the value of b is the sum of the roots taken with the opposite sign: b = -(3 + 2) = -5. The second student copied the constant term and the leading coefficient correctly but the coefficient of x incorrectly, so using the incorrect roots of -6 and 1, the value of c is the product of the roots: c = (-6) times 1 = -6. Thus the correct equation is x2 - 5x - 6 = 0, which factors as (x - 6)(x + 1) = 0, giving the correct roots of 6 and -1.

Keep practicing — related questions