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: A
Explanation
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 = \(\frac{4 \times 25}{64}\) = \(\frac{25}{16}\)
