Question

The absolute value of product of all possible solutions of $2|x{|}^2+5|x|–12=0$, is

• A. $\frac{3}{2}$
  
• B. $\frac{9}{4}$
  
• C. $\frac{9}{16}$
  
• D. $\frac{81}{4}$
  

Answer 1

The correct option is B $\frac{9}{4}$


Consider the equation,
$2|x{|}^2+5|x|-12=0$ ... (i)
Let $|x|=t$
$\Rightarrow 2t^2+5t-12=0$
$\Rightarrow 2t^2+8t-3t-12=0$
$\Rightarrow 2t(t+4)-3(t+4)=0$
$\Rightarrow (2t-3)(t+4)=0$
$\Rightarrow t=\frac{3}{2}$ or $t=-4$
$\Rightarrow |x|=\frac{3}{2}$ or $|x|=-4$
But $|x|$ cannot be negative.
$\therefore |x|=\frac{3}{2}$
$\Rightarrow x=\pm \frac{3}{2}$
Thus, the product of all possible solutions of the given equation is $\frac{3}{2}\times \frac{-3}{2}=\frac{-9}{4}$
And, the absolute value of $\frac{-9}{4}$ is $\frac{9}{4}$
Hence, the correct answer is option (2).