First slide

Theory of equations

Question

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

Easy

A

0
B

1
C

2
D

4

Solution

Given that, $3^{2 x^{2} - 7 x + 7} = 3^{2} \Rightarrow 2 x^{2} - 7 x + 7 = 2$
$\Rightarrow 2 x^{2} - 7 x + 5 = 0$
Now, $D = b^{2} - 4 ac$
$\begin{aligned} = (- 7)^{2} - 4 \times 2 \times 5 \\ = 49 - 40 = 9 > 0 \end{aligned}$
Hence, it has two real roots.

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