Question

Let $\alpha ,\beta$ be the values of m for which the equation $(1+m)x^2-2(1+3m)x+(1+8m)$ has equal roots. Find the equation whose roots are $\alpha +2$ and $\beta +2$.

• A. $x^2-7x+10=0$
• B. $x^2-4x+3=0$
• C. $x^2-5x+6=0$
• D. $x^2-3x=0$

Answer 1

The correct option is A

$x^2-7x+10=0$

$△=0\Rightarrow \left(2\right(1+3m){)}^2-4(1+m\left)\right(1+8m)=0$
$\Rightarrow 1+9m^2+6m-1-9m-8m^2=0$
$\Rightarrow m^2-3m=0$
$\Rightarrow m(m-3)=0$
$\Rightarrow \alpha =0,\beta =3$
$\Rightarrow \alpha +2=2$ and $\beta +2=5$
Equation whose roots are $\alpha +2$ and $\beta +2$ is $(x-2)(x-5)=x^2-7x+10=0$