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WAEC Further Mathematics 2018 Question 9

Question 9

Polynomials

If α and β are the roots of 2x2 − 5x + 6 = 0, find the equation whose roots are (α + 1) and (β + 1).

  1. A.2x2 − 9x − 15
  2. B.2x2 − 9x − 13
  3. C.2x2 − 9x + 13
  4. D.2x2 − 9x − 15
Show the answer and explanation

Answer: C (2x2 − 9x + 13)

Explanation

α + β = 5/2, αβ = 3. New sum = 5/2 + 2 = 9/2; new product = αβ + (α + β) + 1 = 13/2. Equation: x² − (9/2)x + 13/2 = 0, i.e. 2x² − 9x + 13 = 0.