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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations

If α and β are the roots of x² − 5x + 3 = 0, a quadratic equation with roots α/β and β/α is 3x² + px + 3 = 0. What is the value of p?

The value of p is −19. The sum of α/β and β/α is (α²+β²)/αβ = (25−6)/3 = 19/3 and their product is 1. The equation is 3x² − 19x + 3 = 0, so p = −19. Positive 19 ignores the negative sign.

  1. A−19Correct
  2. B−13
  3. C13
  4. D19

Explanation

α+β = 5 and αβ = 3. The sum of new roots = (α²+β²)/(αβ) = (25 − 6)/3 = 19/3 and their product = 1. The equation is x² − (19/3)x + 1 = 0, i.e. 3x² − 19x + 3 = 0, so p = −19. Option 19 forgets the sign change, and −13 uses 25 − 12.

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