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: Option 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})