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Find the quadratic equations whose roots are the reciprocals of the roots of 2x2 + 5x + 3 = 0?

Correct answer: B. 3x2 + 5x + 2 = 0

  • A. 3x2 + 5x - 2 = 0
  • B. 3x2 + 5x + 2 = 0
  • C. 3x2 - 5x + 2 = 0
  • D. 3x2 - 5x - 2 = 0

Explanation

If r is a root of 2r² + 5r + 3 = 0 and z = 1/r, substitute r = 1/z: 2/z² + 5/z + 3 = 0. Multiplying by z² gives 3z² + 5z + 2 = 0, so option b has the reciprocal roots. The likely mistake is choosing option a by changing the constant term incorrectly instead of reversing the coefficients.

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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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