Q. The number of real roots of $3^{2x^{2} - 7x + 7} = 9$ is
A) 0
B) 2
C) 1
D) 4
Explanation
(b)
Given that $3^{2x^{2} - 7x + 7} = 3^{2} \Rightarrow 2x^{2} - 7x + 7 = 2$
$\Rightarrow 2x^{2} + 7x + 5 = 0$
Now, $D = b^{2} - 4ac$
$= ( - 7)^{2} - 4 \times 2 \times 5$
$= 49 - 40 = 9 > 0$
Hence, it has two real roots.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.