Multiple choice

A and B solved a quadratic equation. While solving it, A made a mistake in the constant term and obtained the roots as 5, - 3, while B made a mistake in the coefficient of x and obtained the roots as 1, - 3. The correct roots of the equation are

    • 1, + 3
    • 1, 3
    • 1, - 3

  4. 1, - 1

  5. 1, - 3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's roots (5, -3) give the correct x-coefficient: sum = 2, so x^2 - 2x + c = 0. B's roots (1, -3) give the correct constant: product = -3, so x^2 + bx - 3 = 0. The correct equation is x^2 - 2x - 3 = 0, which factors to (x-3)(x+1) = 0, giving roots 3 and -1.

AI explanation

Using the sum and product of roots, A correctly copied the coefficient of x, giving the correct sum of 5 + (-3) = 2. B correctly copied the constant term, giving the correct product of 1 * (-3) = -3. The correct quadratic equation is therefore x^2 - 2x - 3 = 0. Factoring this gives (x - 3)(x + 1) = 0, meaning the roots are -1 and 3.

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