Question

Meera and Sarika attempted to solve a quadratic equation in $x$ . Sarika made a mistake in reading the coefficient of $x$ and obtained the roots as 12 and 16. Meera made a mistake in reading the constant term of the equation. She obtained the roots as -22 and -6. The correct root(s) is (are) : (A) -16 (B) -12 (C) 12 (D) 16

Choose the correct answer from the options given below:

Accepted Answer

A. Let quadratic equation be $x^2 + bx + c = 0$. Sarika's product of roots is correct: $c = 12 	imes 16 = 192$. Meera's sum of roots is correct: $-b = -22 + (-6) = -28 \implies b = 28$. Correct equation: $x^2 + 28x + 192 = 0 \implies (x + 16)(x + 12) = 0$. Roots are $-16$ and $-12$. So (A) and (B) only.

Mistakes in Quadratic Roots

Explanation

Practise this under exam conditions