First slide

Theory of expressions

Question

$If the expression x^{2} - (5 m - 2) x + (4 m^{2} + 10 m + 25) can be expressed as a perfect square, then m =$

Moderate

A

$\frac{8}{3} or 4$
B

$- \frac{8}{3} or 4$
C

$\frac{4}{3} or 8$
D

$- \frac{4}{3} or 8$

Solution

$x^{2} - (5 m - 2) x + (4 m^{2} + 10 m + 25) can be expressed as a perfect square.$
$∴ Discriminant = 0$
$\begin{array}{ll} ∴ (5 m - 2)^{2} - 4 (4 m^{2} + 10 m + 25) = 0 \\ ∴ 9 m^{2} - 60 m - 96 = 0 \\ ∴ 3 m^{2} - 20 m - 32 = 0 \\ ∴ (3 m + 4) (m - 8) = 0 \\ ∴ m = - 4 / 3, 8 \end{array}$

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