Multiple choice

Which one of the following is the quadratic equation whose roots are reciprocal to the roots of the quadratic equation (2x^2 - 3x - 4 = 0)?

  1. $\(4x^2 + 3x - 2 = 0\)$
  2. $\(5x^2 - 2x - 3 = 0\)$
  3. $\(5x^2 - 8x - 4 = 0\)$
  4. $\(3x^2 - 2x - 4 = 0\)$

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For roots reciprocal to those of 2x² - 3x - 4 = 0, replace x with 1/x: 2(1/x)² - 3(1/x) - 4 = 0 → 2/x² - 3/x - 4 = 0. Multiply by x²: 2 - 3x - 4x² = 0 → 4x² + 3x - 2 = 0. This matches option A.

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