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Mistakes in Quadratic Roots

CMAT 2021 · Quantitative Techniques & Data Interpretation · Medium · Algebra

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Meera and Sarika attempted to solve a quadratic equation in xx. Sarika made a mistake in reading the coefficient of xx 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:

  1. A.

    (A) and (B) only

  2. B.

    (A) and (C) only

  3. C.

    (C) and (D) only

  4. D.

    (B) and (D) only

Answer

A

Explanation

Let quadratic equation be x2+bx+c=0x^2 + bx + c = 0. Sarika's product of roots is correct: c=12×16=192c = 12 \times 16 = 192. Meera's sum of roots is correct: −b=−22+(−6)=−28  ⟹  b=28-b = -22 + (-6) = -28 \implies b = 28. Correct equation: x2+28x+192=0  ⟹  (x+16)(x+12)=0x^2 + 28x + 192 = 0 \implies (x + 16)(x + 12) = 0. Roots are −16-16 and −12-12. So (A) and (B) only.

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