Question

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

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

Answer 1

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

Equation whose roots are k more than roots of
$f\left(x\right)=0$ are $f(x-k)=0.$
$\Rightarrow a(x-2{)}^2+b(x-2)+c=0$
$a(x^2-4x+4)+b(x-2)+c=0$
$a{x}^2+(b-4a)x+4a-2b+c=0.$