Question

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

• A. zero
• B. 2
• C. 1
• D. 4

Answer 1

Answer: (B)

Key Idea : If the discriminant of $a x^{2}+b x+c=0$ is positive, then this equation has two real roots.
We have $ 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 $
$\therefore D =b^{2}-4 a c $
$=(-7)^{2}-4 \times 2 \times 5 $
$ =49-40$
$ =9$
The discriminant of this equation is positive.
Hence, it has two real roots.