Question

state the condition for the quadratic equation ax2+ bx + c is equal to zero to have opposite roots​

Answer 1

$\textbf{Given:}$

$\textsf{Equation is}\;\mathsf{ax^2+bx+c=0}$

$\textbf{To find:}$

$\textsf{The condition for the given quadratic equation}$

$\textsf{has opposite roots}$

$\textbf{Solution:}$

$\textsf{Let the roots of the given equation be}\;\mathsf{\alpha\;and\;-\alpha}$

$\mathsf{Then,}$

$\mathsf{Sum\;of\;the\;roots=\dfrac{-b}{a}}$

$\mathsf{\alpha+(-\alpha)=\dfrac{-b}{a}}$

$\mathsf{0=\dfrac{-b}{a}}$

$\implies\mathsf{-b=0}$

$\implies\boxed{\mathsf{b=0}}$

$\textsf{This is the required condition}$

Answer 2

Answer:

ax^2+c=0is the answer

for the condition of the quadratic equation