Question

Rational roots of the equation $2x^4+x^3-11x^2+x+2=0$ are

• A. $\frac{1}{2},2$
• B. $\frac{1}{2},2,\frac{1}{4},-2$
• C. $\frac{1}{2},2,3,4$
• D. $\frac{1}{2},2,\frac{3}{4},-2$

Answer 1

The correct option is A $\frac{1}{2},2$

This equation can be reduced to a quadratic equation.
$\therefore$ $2x^2+x-11+\frac{1}{x}+\frac{2}{x^2}=0$
$\Rightarrow 2(x^2+\frac{1}{x^2})+(x+\frac{1}{x})-11=0$
Put, $x+\frac{1}{x}=y$
$2(y^2-2)+y-11=0$$\Rightarrow 2y^2+y-15=0$
$\Rightarrow y=-3$ and $\frac{5}{2}$
$\Rightarrow x+\frac{1}{x}=-3,x+\frac{1}{x}=\frac{5}{2}$
$\Rightarrow x^2+3x+1=0,2x^2-5x+2=0$
Only second equation has rational roots as $\frac{1}{2}$ and $2$.