Question

Let $\alpha ,\beta$ be the roots of the equation $(x-a)(x-b)=c,c\ne 0$. Then the roots of the equation $(x-\alpha )(x-\beta )+c=0$ are

• A. $a,c$
• B. $b,c$
• C. $a,b$
• D. $a+c,b+c$

Answer 1

The correct option is C $a,b$

Given $\alpha ,\beta$ are the roots of $(x-a)(x-b)-c=0$

$\Rightarrow (x-a)(x-b)-c=(x-\alpha )(x-\beta )$

$\Rightarrow (x-a)(x-b)=(x-\alpha )(x-\beta )+c$

$\Rightarrow a,b$ are the roots of equation $(x-\alpha )(x-\beta )+c=0$