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UI Post-UTME Mathematics 2014 Question 16

Question 16

Inequalities

For what range of values of p does the equation x2 − px + p + 3 = 0 fail to have real roots?

  1. A.p < 2
  2. B.−2 < p < 6
  3. C.−6 < p < 2
  4. D.p < −2 or p > 6
Show the answer and explanation

Answer: B (−2 < p < 6)

Explanation

No real roots when b² < 4ac: p² < 4(p + 3), i.e. (p − 6)(p + 2) < 0, so −2 < p < 6.