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
\(\frac{5}{4}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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 = \(\frac{4 \times 25}{64}\)
= \(\frac{25}{16}\)
Source: Myschool Past Questions Archive (Record #31548)