Question

If $x=-5$ is a root of $\left|\begin{array}{ccc}2x+1& 4& 8\\ 2& 2x& 2\\ 7& 6& 2x\end{array}\right|=0$ then the other roots are

• A. 3, 3.5
• B. 1, 3.5
• C. 1, 7
• D. 2, 7

Answer 1

Answer: (B)

Given : $\left|\begin{array}{ccc}2x+1& 4& 8\\ 2& 2x& 2\\ 7& 6& 2x\end{array}\right|=0$
$\therefore \left(2x+1\right)\left(4x^2-12\right)-4\left(4x-14\right)+8\left(12-14x\right)=0$
$\Rightarrow 8x^3-24x+4x^2-12-16x+56+96-112x=0$
$\Rightarrow 8x^3+4x^2-152x+140=0$
$\left(x+5\right)$ is a factor of above equation
$\therefore 8x^3+40x^2-36x^2-180x+28x+140=0$
$\Rightarrow 8x^2\left(x+5\right)-36x\left(x+5\right)+28\left(x+5\right)=0$
$\Rightarrow \left(x+5\right)\left(8x^2-36x+28\right)=0$
$\Rightarrow \left(x+5\right)4\left(2x^2-9x+7\right)=0$
$\Rightarrow 4\left(x+5\right)\left(2x^2-7x-2x+7\right)=0$
$\Rightarrow 4\left(x+5\right)\left[x\left(2x-7\right)-1\left(2x-7\right)\right]=0$
$\Rightarrow 4\left(x+5\right)\left(2x-7\right)\left(x-1\right)=0$
$\Rightarrow x=-5,3.5,1$