Question

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

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

Answer 1

Answer: (D)

$9,1$

$a=$ Sum of roots of eq${}^n$ (1)

$\Rightarrow a=-10$

$b=$ prd. of roots of eq${}^n$ $2^{nd}$

$\Rightarrow b=9$

$\therefore$ new eq${}^n$ is $x^2-10x+9=0$

$\Rightarrow (x-1)(x-9)=0$

$\Rightarrow x=1,9$