Question

If $\alpha ,\beta$ are the roots of the equation $x^2+4x-1=0$, then the equation whose roots are $3\alpha -5,3\beta -5$ is

• A. $x^2+22x+76=0$
• B. $x^2+2x-44=0$
• C. $9x^2-18x+4=0$
• D. $x^2+22x-76=0$

Answer 1

The correct option is A $x^2+22x+76=0$

$f\left(x\right)=x^2+4x-1$
$f\left(x\right)=0\to \alpha ,\beta$ are the roots.
Equation whose roots are $3\alpha -5,3\beta -5$ is
$f\left(\frac{x+5}{3}\right)=0$
$\Rightarrow {\left(\frac{x+5}{3}\right)}^2+4\left(\frac{x+5}{3}\right)-1=0\Rightarrow x^2+22x+76=0$