Question

If $\alpha$ and $\beta$ are the roots of $a{x}^2+bx+c=0,$ then $\alpha +\beta =$

• A. $-\frac{c}{a}$
• B. $-\frac{b}{a}$
• C. $\frac{c}{a}$
• D. $\frac{b}{a}$

Answer 1

The correct option is B $-\frac{b}{a}$

$\alpha$ and $\beta$ are roots of the given equation $a{x}^2+bx+c=0$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\alpha =\frac{-b+\sqrt{b^2-4ac}}{2a}$ and

$\beta =\frac{-b-\sqrt{b^2-4ac}}{2a}$

$\alpha +\beta =\frac{-b+\sqrt{b^2-4ac}}{2a}+\left(\frac{-b-\sqrt{b^2-4ac}}{2a}\right)$

$\alpha +\beta =\frac{-2b}{2a}$

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