Find roots of polynomial $$ p(x) = 8x^4+25x $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0\\[1 em]x_2 &= -1.462\\[1 em]x_3 &= 0.731+1.2661i\\[1 em]x_4 &= 0.731-1.2661i \end{aligned} $$Explanation
Step 1:
Factor out $ \color{blue}{ x }$ from $ 8x^4+25x $ and solve two separate equations:
$$ \begin{aligned} 8x^4+25x & = 0\\[1 em] \color{blue}{ x }\cdot ( 8x^3+25 ) & = 0 \\[1 em] \color{blue}{ x = 0} ~~ \text{or} ~~ 8x^3+25 & = 0 \end{aligned} $$One solution is $ \color{blue}{ x = 0 } $. Use second equation to find the remaining roots.
Step 2:
Polynomial $ 8x^3+25 $ 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