Question

If $\alpha ,\beta$ are the roots of $2x^2+3x+1=0$, then the equation whose roots are $\frac{1}{\alpha },\frac{1}{\beta }$ is

• A. $x^2+3x+2=0$
• B. $x^2-3x+2=0$
• C. $2x^2+x+1=0$
• D. $2x^2-x+1=0$

Answer 1

The correct option is A $x^2+3x+2=0$

$f\left(x\right)=2x^2+3x+1=0\text{has roots}\alpha ,\beta$
The equation whose roots are $\frac{1}{\alpha },\frac{1}{\beta }$ is,
$f\left(\frac{1}{x}\right)=0$
$\Rightarrow \frac{2}{x^2}+\frac{3}{x}+1=0\Rightarrow 2+3x+x^2=0\Rightarrow x^2+3x+2=0$