Question

Question 7
If b = 0, c <0, is it true that the roots of $x^2$ + bx + c = 0 are numerically equal and opposite in sign ? Justify your answer.

Answer 1

Given that, b = 0 and c < 0 and quadratic equation $x^2+bx+c=0$
put b = 0 in Eq. (i), we get
$x^2$ + 0 + c = 0
$\Rightarrow x^2=-c$ [here c > 0 ]
$x=\pm \sqrt{-c}$ [ $\because$ c > 0]
so, the roots of $x^2$ + bx + c = 0 are numerically equal and opposite in sign.