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WAEC Further Mathematics 2022 Question 36

Question 36

Polynomials

If α and β are the roots of x2 + mx − n = 0, where m and n are constants, form the equation whose roots are 1/α and 1/β.

  1. A.mnx2 − n2x − m = 0
  2. B.mx2 − nx + 1 = 0
  3. C.nx2 − mx + 1 = 0
  4. D.nx2 − mx − 1 = 0
Show the answer and explanation

Answer: D (nx2 − mx − 1 = 0)

Explanation

α + β = −m, αβ = −n. New sum = (α + β)/αβ = m/n, new product = 1/αβ = −1/n. So x² − (m/n)x − 1/n = 0, i.e. nx² − mx − 1 = 0.