Question

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

• A. $x^2-6x+11=0$
• B. $x^2-5x+10=0$
• C. $x^2+6x-11=0$
• D. None of these

Answer 1

The correct option is A $x^2-6x+11=0$

$\alpha$ and $\beta$ are the roots of the equation $x^2-2x+3=0$.
let $y=\alpha +2$
$\Rightarrow \alpha =y-2$
$\Rightarrow (y-2{)}^2-2(y-2)+3=0$
$\Rightarrow y^2-6y+11=0$
$\therefore$ Equation whose roots are $\alpha +2$,$\beta +2$ is $x^2-6x+11=0$
Hence, option A.