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JAMB Mathematics 1979 Question 30

Question 30

Polynomials

If x3 − 12x − 16 = 0 has x = −2 as a solution, then the equation has

  1. A.x = −4 as a solution also
  2. B.3 roots all different
  3. C.3 roots with two equal and the third different
  4. D.3 roots all equal
  5. E.only one root.
Show the answer and explanation

Answer: C (3 roots with two equal and the third different)

Explanation

Dividing by (x + 2) gives x² − 2x − 8 = (x + 2)(x − 4), so x³ − 12x − 16 = (x + 2)²(x − 4). The roots are −2, −2 and 4.