Question

Find the roots of the following quadratic equation

$z^2+6z-8=0$

• A. $z=-3\pm \sqrt{19}$
• B. $z=-3\pm \sqrt{17}$
• C. $z=-2\pm \sqrt{17}$
• D. $z=-3\pm \sqrt{15}$

Answer 1

The correct option is B $z=-3\pm \sqrt{17}$

The roots of the quadratic equation $a{x}^2+bx+c=0$ are

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

So, the roots of $z^2+6z-8=0$ are

$z=\frac{-6\pm \sqrt{6^2-4\left(1\right)(-8)}}{2}$

$\therefore z=\frac{-6\pm \sqrt{68}}{2}$

$\therefore z=\frac{-6\pm 2\sqrt{17}}{2}$

$\therefore z=-3\pm \sqrt{17}$