JAMB 1989 · UME · Q24

Quadratics & their graphs

What value of $Q$ will make the expression $4x^2 + 5x + Q$ a complete square?

Worked solution (try it first)

A complete square with $4x^2$ has the form $(2x + k)^2 = 4x^2 + 4kx + k^2$ .
Match the $x$ terms: $4k = 5$ , so $k = \frac54$ .
So $Q = k^2 = \frac{25}{16}$ , option A.

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