Find the values of m which make the following quadratic function a perfect square. x2...

Mathematics

JAMB 1987

Find the values of m which make the following quadratic function a perfect square. x² + 2(m + 1)x + m + 3

A. -1, 1
B. -1, 2
C. 1, -2
D. 2, -2

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Correct Answer: Option C

Explanation

x² + 2(m + 1)x + m + 3 from (A + B)² = a² + 2AB + b²

2B = \(\frac{2(m + 1)}{2}\) = m + 1 .......(i)

Also B² = m + 3..........(ii)

Subst. for B in equation ..........(iii)

= (m + 1)² = m + 3 = m² + 2m + 1 = m + 3

= m² + 2m - m + 1 - 3 = 0

m² + m - 2 = 0

(m + 2)(m - 1) = 0 or m - 1 = 0

m = -2 or 1

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