Find roots of polynomial $$ p(x) = -\frac{835}{12}x^4+\frac{1027}{2}x^3-\frac{12749}{12}x^2+\frac{1231}{2}x+206 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.2315\\[1 em]x_2 &= 4.4028\\[1 em]x_3 &= 1.6042+0.5755i\\[1 em]x_4 &= 1.6042-0.5755i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 12 } $.
$$ \begin{aligned} -\frac{835}{12}x^4+\frac{1027}{2}x^3-\frac{12749}{12}x^2+\frac{1231}{2}x+206 & = 0 ~~~ / \cdot \color{blue}{ 12 } \\[1 em] -835x^4+6162x^3-12749x^2+7386x+2472 & = 0 \end{aligned} $$Step 2:
Polynomial $ -835x^4+6162x^3-12749x^2+7386x+2472 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
This page was created using
Polynomial Roots Calculator