Question

find the sum of the solutions of this equation 5x^2+3x+8=0

Answer 1

Hey Jamae,
to solve this there is a simple formula that works with every polynomial of the form \(ax^2+bx+c = 0\)
\[
x_{1,2} = \frac{1}{2a} \left[ -b \pm\sqrt{b²-4ac} \right]
\]

For your equation this means the following:
\[
\underbrace{5}_{a}x^2+\underbrace{3}_{b}x+\underbrace{8}_c = 0
\]
if you plug your values in, you get the following:
\[
x_{1,2} = \frac{1}{10}\left( - 3 \pm \sqrt{9-4\cdot5\cdot8} \right) =
\frac{1}{10}\left( - 3 \pm \sqrt{9-4\cdot5\cdot8} \right)
\]
\[
= \frac{1}{10}\left( - 3 \pm \sqrt{-151} \right)
\]
\[
\Rightarrow x_1 =- \frac{1}{10}\mathbf{i}\left( \sqrt{151} - 3 \mathbf{i} \right),
\quad x_1 = \frac{1}{10}\mathbf{i}\left( \sqrt{151}+ 3 \mathbf{i} \right)
\]