What value of Q will make the expression 4x2 + 5x + Q a complete square?
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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 = \(\frac{4 \times 25}{64}\)
= \(\frac{25}{16}\)
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 = \(\frac{4 \times 25}{64}\)
= \(\frac{25}{16}\)