Question

If $\alpha ,\beta$ are the roots of quadratic equation $x^2+3x+8=0$. Find the equation with roots $\alpha -5$ and $\beta -5$

• A. $x^2+13x+40=0$
• B. $x^2+15x+56=0$
• C. $x^2+13x+48=0$
• D. $x^2+11x+36=0$

Answer 1

The correct option is C $x^2+13x+48=0$

A quadratic equation $a{x}^2+bx+c=0$ with roots $\alpha ,\beta$ is transformed for the roots $\alpha -k$ and $\beta -k$ where $k\in R$,
is given by $a(x-k{)}^2+b(x-k)+c=0$

Here, $a=1,b=3,c=8,k=5$

$\therefore 1(x+5{)}^2+3(x+5)+8=0$

$\Rightarrow x^2+10x+25+3x+15+8=0$

$\Rightarrow x^2+13x+48=0$

Hence, required quadratic equation is $x^2+13x+48=0$