Question

The roots of the following quadratic equation
$9a^2{b}^2{x}^2$ - 24abcdx + $16c^2{d}^2$ = 0, a $\ne$ 0, b $\ne$ 0 are Real and equal.

• A. True
• B. False

Answer 1

The correct option is A True

$\Rightarrow$ $9a^2{b}^2{x}^2-24abcdx+16c^2{d}^2=0$

$\Rightarrow$ Here, $A=9a^2{b}^2,B=-24abcd,C=16c^2$

$\Rightarrow$ $B^2-4AC$

$\Rightarrow$ $(-24abc)-4\left(9a^2{b}^2\right)\left(16c^2{d}^2\right)$

$\Rightarrow$ $576a^2{b}^2{c}^2{d}^2-576a^2{b}^2{c}^2{d}^2$

$\Rightarrow$ $0$

$\therefore$ $Discriminant=0$

$\Rightarrow$ Hence, roots of given quadratic equation are real and equal.