Find roots of polynomial $$ p(x) = t^4-8t^2+16t $$
Answer
The roots of polynomial $ p(t) $ are:
$$ \begin{aligned}t_1 &= 0\\[1 em]t_2 &= -3.5386\\[1 em]t_3 &= 1.7693+1.1795i\\[1 em]t_4 &= 1.7693-1.1795i \end{aligned} $$Explanation
Step 1:
Factor out $ \color{blue}{ t }$ from $ t^4-8t^2+16t $ and solve two separate equations:
$$ \begin{aligned} t^4-8t^2+16t & = 0\\[1 em] \color{blue}{ t }\cdot ( t^3-8t+16 ) & = 0 \\[1 em] \color{blue}{ t = 0} ~~ \text{or} ~~ t^3-8t+16 & = 0 \end{aligned} $$One solution is $ \color{blue}{ t = 0 } $. Use second equation to find the remaining roots.
Step 2:
Polynomial $ t^3-8t+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