Question

If $\alpha ,\beta$ 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 $a{x}^2+x(b-4a)+4a-2b+c=0$

The equation will be
$x^2-(\alpha +\beta +4)x+(\alpha \beta +4+2(\alpha +\beta \left)\right)=0$
From the first equation, we know the products and the sum of the roots.
Hence, we substitute it in the equation
$x^2-(4-\frac{b}{a})x+(4+\frac{c-2b}{a})=0$
$a{x}^2+(b-4a)x+(c-2b+4a)=0$