Question

If $2,8$ are the roots of $x^2+ax+\beta =0$ and $3,3$ are the roots of $x^2+\alpha x+b=0$ then find the roots of $x^2+ax+b=0$.

• A. $-1,-9$
• B. $1,9$
• C. $-2,-8$
• D. $2,8$

Answer 1

The correct option is B $1,9$

Given $2,8$ are the roots of the equation $x^2+ax+\beta =0$.

Then form the relation of roots and co-efficients we get,

$a=-10$ and $\beta =16$........(1).

Also given $3,3$ are the roots of the equation $x^2+\alpha x+b=0$.

Then from the relation between the roots and co-efficients we get,

$\alpha =-6$ and $b=9$.......(2).

Using values of $a$ and $b$ the equation $x^2+ax+b=0$ will take the form,

$x^2-10x+9=0$

or, $(x-1)(x-9)=0$

or, $x=1,9$.

The required roots are $1,9$