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

\frac{8}{3}

4

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- \frac{8}{3}

4

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\frac{4}{3}

8

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- \frac{4}{3}

8

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Solution

The correct option is D $- \frac{4}{3}$ or $8$
$x^{2} - (5 m - 2) x + 4 m^{2} + 10 m + 25 = 0$
is perfect square.
$∴ D = 0$
$(5 m - 2)^{2} - 4 (4 m^{2} + 10 m + 25) = 0$
$25 m^{2} + 4 - 20 m - 16 m^{2} - 40 m - 100 = 0$
$9 m^{2} - 60 m - 96 = 0$
$m = 8$ and - $\frac{4}{3}$

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Identify the greater number, wherever possible, in each of the following?

(i) 4³ or 3⁴ (ii) 5³ or 3⁵

(iii) 2⁸ or 8² (iv) 100²or 2¹⁰⁰

(v) 2¹⁰ or 10²

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