Find roots of polynomial $p (x) = x^{4} - 13 x$

Answer

The roots of polynomial $p (x)$ are:
$x_{1} x_{2} x_{3} x_{4} = 0 = 2.3513 = - 1.1757 + 2.0363 i = - 1.1757 - 2.0363 i$

Explanation

Step 1:

Factor out $x$ from $x^{4} - 13 x$ and solve two separate equations:

x^{4} - 13 x x \cdot (x^{3} - 13) x = 0 or x^{3} - 13 = 0 = 0 = 0

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

Step 2:

Polynomial $x^{3} - 13$ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.

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Find roots of polynomial p(x)=x4−13x

The roots of polynomial p(x) are: x1​x2​x3​x4​​=0=2.3513=−1.1757+2.0363i=−1.1757−2.0363i​

Find roots of polynomial $p (x) = x^{4} - 13 x$

The roots of polynomial $p (x)$ are:
$x_{1} x_{2} x_{3} x_{4} = 0 = 2.3513 = - 1.1757 + 2.0363 i = - 1.1757 - 2.0363 i$