Question

use the quadratic formula to solve the quadratic equation 10z² + 5z = 5z - 8. express the solutions in the form a ± bi. (1 point) o 0 ± 2√5/5 i o -1/2 ± √55/10 i o 2√5/5 ± 0i o 1/2 + √22/1 i

Explanation:

Step1: Rewrite the quadratic equation in standard form

First, rewrite $10z^{2}+5z = 5z - 8$ as $10z^{2}+8 = 0$. Here $a = 10$, $b = 0$, $c = 8$.

Step2: Apply the quadratic formula

The quadratic formula is $z=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute $a = 10$, $b = 0$, $c = 8$ into it: $z=\frac{0\pm\sqrt{0 - 4\times10\times8}}{2\times10}=\frac{\pm\sqrt{- 320}}{20}$.

Step3: Simplify the square - root of the negative number

We know that $\sqrt{-320}=\sqrt{320}\times\sqrt{- 1}=\sqrt{64\times5}\times i = 8\sqrt{5}i$. So $z=\frac{\pm8\sqrt{5}i}{20}=\pm\frac{2\sqrt{5}}{5}i$.

Answer:

$0\pm\frac{2\sqrt{5}}{5}i$