Find roots of polynomial $p (x) = x^{6} + x^{5} + x^{4} + x^{3} + 7 x^{2} + 5 x + 2$

Answer

The roots of polynomial $p (x)$ are:
$x_{1} x_{2} x_{3} x_{4} x_{5} x_{6} = - 0.3754 + 0.4122 i = - 0.3754 - 0.4122 i = - 1.1332 + 1.1282 i = - 1.1332 - 1.1282 i = 1.0085 + 1.2245 i = 1.0085 - 1.2245 i$

Explanation

Polynomial $x^{6} + x^{5} + x^{4} + x^{3} + 7 x^{2} + 5 x + 2$ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.

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Find roots of polynomial p(x)=x6+x5+x4+x3+7x2+5x+2

The roots of polynomial p(x) are: x1​x2​x3​x4​x5​x6​​=−0.3754+0.4122i=−0.3754−0.4122i=−1.1332+1.1282i=−1.1332−1.1282i=1.0085+1.2245i=1.0085−1.2245i​

Find roots of polynomial $p (x) = x^{6} + x^{5} + x^{4} + x^{3} + 7 x^{2} + 5 x + 2$

The roots of polynomial $p (x)$ are:
$x_{1} x_{2} x_{3} x_{4} x_{5} x_{6} = - 0.3754 + 0.4122 i = - 0.3754 - 0.4122 i = - 1.1332 + 1.1282 i = - 1.1332 - 1.1282 i = 1.0085 + 1.2245 i = 1.0085 - 1.2245 i$