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OAU Post-UTME Mathematics 2021 (Batch B) Question 5

Question 5

Quadratic Equations

If α and β are the roots of 7x2 − x(x + 13) = 15, find the value of 1/(α + 1) + 1/(β + 1).

  1. A.25/4
  2. B.4/25
  3. C.6/4
  4. D.4/6
Show the answer and explanation

Answer: A (25/4)

Explanation

The equation is 6x² − 13x − 15 = 0, so α + β = 13/6 and αβ = −15/6. The sum = (α + β + 2)/(αβ + α + β + 1) = (25/6)/(4/6) = 25/4.