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Match Quadratic Equations with Roots

CMAT 2025 · Quantitative Techniques & Data Interpretation · Medium · Quantitative Aptitude

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Match List I with List II :

List I (Quadratic equations) (A) 12x2−7x+1=012x^2 - 7x + 1 = 0 (B) 20x2−9x+1=020x^2 - 9x + 1 = 0 (C) x2+17x+52=0x^2 + 17x + 52 = 0 (D) 2x2+11x+12=02x^2 + 11x + 12 = 0

List II (Roots) (I) {−13,−4}\{-13, -4\} (II) {13,14}\{\frac{1}{3}, \frac{1}{4}\} (III) {−4,−32}\{-4, -\frac{3}{2}\} (IV) {15,14}\{\frac{1}{5}, \frac{1}{4}\}

Choose the correct answer from the options given below :

  1. A.

    (A)-(II), (B)-(I), (C)-(III), (D)-(IV)

  2. B.

    (A)-(II), (B)-(III), (C)-(IV), (D)-(I)

  3. C.

    (A)-(II), (B)-(IV), (C)-(III), (D)-(I)

  4. D.

    (A)-(II), (B)-(IV), (C)-(I), (D)-(III)

Answer

D

Explanation

  • (A) 12x2−7x+1=0  ⟹  (3x−1)(4x−1)=0  ⟹  x={13,14}12x^2 - 7x + 1 = 0 \implies (3x-1)(4x-1) = 0 \implies x = \left\{\frac{1}{3}, \frac{1}{4}\right\} (II)
  • (B) 20x2−9x+1=0  ⟹  (4x−1)(5x−1)=0  ⟹  x={15,14}20x^2 - 9x + 1 = 0 \implies (4x-1)(5x-1) = 0 \implies x = \left\{\frac{1}{5}, \frac{1}{4}\right\} (IV)
  • (C) x2+17x+52=0  ⟹  (x+13)(x+4)=0  ⟹  x={−13,−4}x^2 + 17x + 52 = 0 \implies (x+13)(x+4) = 0 \implies x = \{-13, -4\} (I)
  • (D) 2x2+11x+12=0  ⟹  (x+4)(2x+3)=0  ⟹  x={−4,−32}2x^2 + 11x + 12 = 0 \implies (x+4)(2x+3) = 0 \implies x = \left\{-4, -\frac{3}{2}\right\} (III)

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