What value of Q will make the expression 4x2 + 5x + Q a complete square?

A.

\(\frac{25}{16}\)

B.

\(\frac{25}{64}\)

C.

\(\frac{5}{8}\)

D.

\(\frac{5}{4}\)

Correct answer is A

4x2 + 5x + Q

To make a complete square, the coefficient of x2 must be 1

= x2 + \(\frac{5x}{4}\) + \(\frac{Q}{4}\)

Then (half the coefficient of x2) should be added

i.e. x2 + \(\frac{5x}{4}\) + \(\frac{25}{64}\)

∴ \(\frac{Q}{4}\) = \(\frac{25}{64}\)

Q = \(\frac{4 \times 25}{64}\)

= \(\frac{25}{16}\)