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WAEC Further Mathematics 2010 Question 7

Question 7

Polynomials

The roots of a quadratic equation are (3 − √3) and (3 + √3). Find its equation.

  1. A.x2 − 6x − 9 = 0
  2. B.x2 − 6x + 6 = 0
  3. C.x2 + 6x − 9 = 0
  4. D.x2 + 6x + 6 = 0
Show the answer and explanation

Answer: B (x2 − 6x + 6 = 0)

Explanation

Sum of roots = 6 and product = (3 − √3)(3 + √3) = 9 − 3 = 6. The equation is x2 − (sum)x + product = 0, i.e. x2 − 6x + 6 = 0.