What value of Q will make the expression 4×2 + 5x + Q a complete…

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

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