Question

If $a$ and $b$ are the roots of the equation $x^2+ax-b=0$, then find $a$ and $b$.

Answer 1

Given that $a$ and $b$ are the roots of equation $x^2+ax-b=0$.

Here, $A=1,B=a,C=-b$

Now,

Sum of roots $=\frac{-B}{A}$

$\to a+b=\frac{-a}{1}$

$\Rightarrow a+b=-a$

$\Rightarrow b=-2a.....\left(1\right)$

Now,

Product of roots $=\frac{C}{A}$

$a\times b=\frac{-b}{1}$

$\Rightarrow a\times b=-b$

$\Rightarrow a=-1$

Substituting the value of $a$ in equation $\left(1\right)$, we have

$b=-2\times (-1)=2$

Hence the value of $a$ and $b$ are$-1$ and $2$ respectively.