Question

The sum of non-integeral roots of the equation $x^4-3x^3-2x^2+3x+1=0$ is

• A. $3$
• B. $0$
• C. $-3$
• D. $6$

Answer 1

The correct option is A $3$

Divide the given equation by $x^2$$\Rightarrow x^2-3x-2+\frac{3}{x}+\frac{1}{x^2}=0$
$\Rightarrow (x^2+\frac{1}{x^2})-3(x-\frac{1}{x})-2=0$
Now put $x-\frac{1}{x}=y$
$\Rightarrow (y^2+2)-3y-2=0\Rightarrow y^2-3y=0\Rightarrow y=0,3$
Case $I$:
$x-\frac{1}{x}=0\Rightarrow x=\pm 1$
Case $II$: $x-\frac{1}{x}=3\Rightarrow x=\frac{1}{2}(3\pm \sqrt{13})$