Question

If $\alpha ,\beta$ are the roots of $2x^2+3x+4=0$, then the equation whose roots are $2\alpha ,2\beta$ is

• A. $x^2+3x+4=0$
• B. $x^2+3x+8=0$
• C. $4x^2+3x+4=0$
• D. $4x^2+3x+2=0$

Answer 1

The correct option is B $x^2+3x+8=0$

$f\left(x\right)=2x^2+3x+4f\left(x\right)=0\to \alpha ,\beta \text{are the roots}$
The equation whose roots are $2\alpha ,2\beta$ is,
$f\left(\frac{x}{2}\right)=0$
$\Rightarrow 2{\left(\frac{x}{2}\right)}^2+3\left(\frac{x}{2}\right)+4=0\Rightarrow x^2+3x+8=0$