Question Bank • QB_GA_QA_018 MSQ • 2 Marks

Section 8: General Aptitude

Quantitative Aptitude

Subtopic: Numerical Computation

Question Statement:

Consider the quadratic equation $x^2 - 12x + 35 = 0$. Which of the following statements regarding its roots is/are correct?

Options:

  • (A) Both roots are positive integers.
  • (B) The sum of the roots is 12.
  • (C) The product of the roots is 35.
  • (D) The absolute difference between the roots is 3.

Answer Key:

A, B, C

Step-by-Step Solution & Explanation

1. Factorize the quadratic polynomial: $x^2 - 12x + 35 = (x - 7)(x - 5) = 0$ Roots are $x_1 = 7$ and $x_2 = 5$. 2. Verification of statements: • A: 5 and 7 are both positive integers (Correct). • B: Sum of roots $= 7 + 5 = 12$ (Correct). • C: Product of roots $= 7 \times 5 = 35$ (Correct). • D: Absolute difference $= |7 - 5| = 2 \ne 3$ (Incorrect).
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