Question

If $\alpha ,\beta$ are the roots of quadratic equation $x^2+7x+10=0$. Then the quadratic equation with roots as $\alpha +2$ and $\beta +2$ is

• A. $x^2+3x+10=0$
• B. $x^2+3x=0$
• C. $x^2+7x+18=0$
• D. $x^2+11x+18=0$

Answer 1

The correct option is B $x^2+3x=0$

We know that if a quadratic equation $a{x}^2+bx+c=0$ with roots $\alpha ,\beta$ are transformed the roots $\alpha +k$ and $\beta +k$ where k is any costant then,
quadratic eqution is $a(x-k{)}^2+b(x-k)+c=0$

Here, $a=1,b=7,c=10,k=2$

$\therefore 1(x-2{)}^2+7(x-2)+10=0$

$\Rightarrow x^2-4x+4+7x-14+10=0$

$\Rightarrow x^2+3x+0=0$

Hence, the required quadratic equation is $x^2+3x=0$