Find roots of polynomial $$ p(x) = 10x-8-15x^2-24x^3+5x^4 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.0687\\[1 em]x_2 &= 5.3051\\[1 em]x_3 &= 0.2818+0.4503i\\[1 em]x_4 &= 0.2818-0.4503i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 10x-8-15x^2-24x^3+5x^4 & = 0\\[1 em] 5x^4-24x^3-15x^2+10x-8 & = 0 \end{aligned} $$Step 2:
Polynomial $ 5x^4-24x^3-15x^2+10x-8 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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