The number of real roots of $3^{2 x^{2} - 7 x + 7} = 9$ is :

zero

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Solution

The correct option is B 2
$3^{2 x^{2} - 7 x + 7} = 9 \Rightarrow 3^{2 x^{2} - 7 x + 7} = 3^{2}$
$\Rightarrow 2^{x^{2}} - 7 x + 7 = 2 \Rightarrow 2^{x^{2}} - 7 x + 5 = 0$
Here Discriminant $= (- 7)^{2} - 4 (2) (5) = 49 - 40 = 9 > 0$
Hence the given equation has two real roots.

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