Find roots of polynomial $p (x) = 2 x^{3} - 4 x^{2} - 3 x^{6}$

Answer

The roots of polynomial $p (x)$ are:
$x_{1} x_{2} x_{3} x_{4} x_{5} = 0 = 0.7665 + 0.6083 i = 0.7665 - 0.6083 i = - 0.7665 + 0.8972 i = - 0.7665 - 0.8972 i$

Explanation

Step 1:

Write polynomial in descending order

2 x^{3} - 4 x^{2} - 3 x^{6} - 3 x^{6} + 2 x^{3} - 4 x^{2} = 0 = 0

Step 2:

Factor out $- x^{2}$ from $- 3 x^{6} + 2 x^{3} - 4 x^{2}$ and solve two separate equations:

- 3 x^{6} + 2 x^{3} - 4 x^{2} - x^{2} \cdot (3 x^{4} - 2 x + 4) - x^{2} = 0 or 3 x^{4} - 2 x + 4 = 0 = 0 = 0

One solution is $x = 0$ . Use second equation to find the remaining roots.

Step 3:

Polynomial $3 x^{4} - 2 x + 4$ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.

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Find roots of polynomial p(x)=2x3−4x2−3x6

The roots of polynomial p(x) are: x1​x2​x3​x4​x5​​=0=0.7665+0.6083i=0.7665−0.6083i=−0.7665+0.8972i=−0.7665−0.8972i​

Find roots of polynomial $p (x) = 2 x^{3} - 4 x^{2} - 3 x^{6}$

The roots of polynomial $p (x)$ are:
$x_{1} x_{2} x_{3} x_{4} x_{5} = 0 = 0.7665 + 0.6083 i = 0.7665 - 0.6083 i = - 0.7665 + 0.8972 i = - 0.7665 - 0.8972 i$