If b = 0, c < 0, is it true that the roots

Question:

If b = 0, c < 0, is it true that the roots of x2 + bx + c = 0 are numerically equal and opposite in sign? Justify your answer.

Solution:

Given that, b = 0andc < 0and quadratic equation,

$x^{2}+b x+c=0$ $\ldots(i)$

Put $b=0$ in Eq. (i), we get

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

$\Rightarrow$ $x^{2}=-c$   $\left[\begin{array}{l}\text { here } c>0 \\ \therefore-c>0\end{array}\right]$

$\therefore$ $x=\pm \sqrt{-C}$

So, the roots of x2 + bx+c = O are numerically equal and opposite in sign.

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