Question

If the roots of equation $a{x}^2+bx+c=0$ are equal in magnitude but opposite in sign then the value of $b$ will be.

Answer 1

Compute the required value:

Given: The roots of the equation $a{x}^2+bx+c=0$ are equal in magnitude but opposite in sign.

Let us assume two roots of the equations are $\alpha$ and $\beta$.

Therefore, $\alpha =-\beta$

Since, sum of roots$=-\frac{b}{a}$

$\Rightarrow$ $\alpha +\beta =-\frac{b}{a}$

$\Rightarrow$ $-\beta +\beta =-\frac{b}{a}$

$\Rightarrow$ $0=-b$

$\Rightarrow$ $b=0$

Hence the value of $b$ is $0.$