Find roots of polynomial $$ p(x) = 2x^3+13x+6x-45 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.7774\\[1 em]x_2 &= -0.8887+3.4452i\\[1 em]x_3 &= -0.8887-3.4452i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ 2x^3+ \color{blue}{13x} + \color{blue}{6x} -45 = 2x^3+ \color{blue}{19x} -45 $$Step 2:
Polynomial $ 2x^3+19x-45 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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