Question

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

• A. zero
• B. 2
• C. 1
• D. 4

Answer 1

Answer: (B)

Key Idea : If the discriminant of $a{x}^2+bx+c=0$ is positive, then this equation has two real roots.
We have $3^{2x^2-7x+7}=3^2$
$\Rightarrow 2x^2-7x+7=2$
$\Rightarrow 2x^2-7x+5=0$
$\therefore D=b^2-4ac$
$=(-7{)}^2-4\times 2\times 5$
$=49-40$
$=9$
The discriminant of this equation is positive.
Hence, it has two real roots.