Find roots of polynomial $$ p(x) = 3x^4-7x^3-9x+2+24x-4 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.1344\\[1 em]x_2 &= -1.244\\[1 em]x_3 &= 1.7215+1.0119i\\[1 em]x_4 &= 1.7215-1.0119i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ 3x^4-7x^3 \color{blue}{-9x} + \color{red}{2} + \color{blue}{24x} \color{red}{-4} = 3x^4-7x^3+ \color{blue}{15x} \color{red}{-2} $$Step 2:
Polynomial $ 3x^4-7x^3+15x-2 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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