The roots of the equation $3^{2 x} - {10.3}^{x} + 9 = 0$ are

1, 2

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0, 2

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0, 1

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1, 3

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Solution

The correct option is D $0, 2$
$(3^{x})^{2} - {10.3}^{x} + 9 = 0$
Let $3^{x} = t$
$\Rightarrow t^{2} - 10 t + 9 = 0$
$\Rightarrow t^{2} - 9 t - t + 9 = 0$
$\Rightarrow t (t - 9) - (t - 9) = 0$
$\Rightarrow (t - 1) (t - 9) = 0$
$t = 1, 9$
$3^{x} = 1 = 3^{0} \Rightarrow x = 0$
and $3^{x} = 93^{2} \Rightarrow x = 2$
$∴ x = 0, 2$

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The roots of the equation $3^{2 x} - {10.3}^{x} + 9 = 0$ are

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