Find roots of polynomial $$ p(x) = -5x^4+3x^2+8x $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0\\[1 em]x_2 &= 1.3396\\[1 em]x_3 &= -0.6698+0.8636i\\[1 em]x_4 &= -0.6698-0.8636i \end{aligned} $$Explanation
Step 1:
Factor out $ \color{blue}{ -x }$ from $ -5x^4+3x^2+8x $ and solve two separate equations:
$$ \begin{aligned} -5x^4+3x^2+8x & = 0\\[1 em] \color{blue}{ -x }\cdot ( 5x^3-3x-8 ) & = 0 \\[1 em] \color{blue}{ -x = 0} ~~ \text{or} ~~ 5x^3-3x-8 & = 0 \end{aligned} $$One solution is $ \color{blue}{ x = 0 } $. Use second equation to find the remaining roots.
Step 2:
Polynomial $ 5x^3-3x-8 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
This page was created using
Polynomial Roots Calculator