Question

Roots are additive inverse of each other than _________________ is true.

Answer 1

Given,

Roots of a quadratic equation are additive inverse of each other.

Let, the roots are $x_{1}and{x}_2$

Then, $x_1+x_2=0....\left(1\right)$

and, we know that for a polynomial:

$a{x}^2+bx+c=0$

The sum of its roots is given by:

$x_1+x_2=-\frac{b}{a}...\left(2\right)$

Hence, from equation (1) and (2) we have

$\frac{b}{a}=0$

Hence, $b=0....\left(3\right)$

$\text{Roots are additive of each other than coefficent of x is equals to zero(i.e., b=0) is true}$