Find roots of polynomial $$ p(x) = 5x^4-9x^2+16x $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0\\[1 em]x_2 &= -1.8731\\[1 em]x_3 &= 0.9365+0.9118i\\[1 em]x_4 &= 0.9365-0.9118i \end{aligned} $$Explanation
Step 1:
Factor out $ \color{blue}{ x }$ from $ 5x^4-9x^2+16x $ and solve two separate equations:
$$ \begin{aligned} 5x^4-9x^2+16x & = 0\\[1 em] \color{blue}{ x }\cdot ( 5x^3-9x+16 ) & = 0 \\[1 em] \color{blue}{ x = 0} ~~ \text{or} ~~ 5x^3-9x+16 & = 0 \end{aligned} $$One solution is $ \color{blue}{ x = 0 } $. Use second equation to find the remaining roots.
Step 2:
Polynomial $ 5x^3-9x+16 $ 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