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Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 8x + 4 = 0?

Correct answer: B. 14

  • A. 15
  • B. 14
  • C. 24
  • D. 26

Explanation

For x² + 8x + 4 = 0, Vieta's relations give a + b = -8 and ab = 4. Therefore a/b + b/a = (a² + b²)/ab = ((a + b)² - 2ab)/ab = (64 - 8)/4 = 56/4 = 14. The likely mistake is choosing a, which comes from using (a + b)²/ab and forgetting to subtract 2ab.

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About Quadratic Equations

Quadratic equations contain a squared variable and can be solved by factorisation, completing the square, the quadratic formula, or graphical reasoning. Questions cover roots, the discriminant, and the relationship between roots and coefficients, while distinguishing real and repeated roots from complex or non-real roots.

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