Question

If $\alpha ,\beta$ are the roots of $a{x}^2+bx+c=0$, the equation whose roots are $2+\alpha ,2+\beta$ is

• A. $a{x}^2+(4a-b)x+4a+2b+c=0$
• B. $a{x}^2+(4a-b)x+4a-2b+c=0$
• C. $a{x}^2+(b-4a)x+4a+2b+c=0$
• D. $a{x}^2+(b-4a)x+4a-2b+c=0$

Answer 1

The correct option is D $a{x}^2+(b-4a)x+4a-2b+c=0$

Given: $\alpha ,\beta$ are the roots of $a{x}^2+bx+c=0$.

Using the concept of transformation of equation, we have to replace $x$ by $(x–2)$ to get equation whose roots are $\alpha +2,\beta +2.$
We get,
$\Rightarrow a(x-2{)}^2+b(x-2)+c=0$
$\Rightarrow a{x}^2-(4a-b)x+4a+c–2b=0$

$\therefore$ The required quadratic equation is
$a{x}^2+(b-4a)x+4a-2b+c=0$