Find roots of polynomial $p (x) = 42 x^{6} - 12 x^{5} + 20 x^{4} + 8 x^{3} - 3000000 x^{2} + 18 x + 1$

Answer

The roots of polynomial $p (x)$ are:
$x_{1} x_{2} x_{3} x_{4} x_{5} x_{6} = - 0.0006 = 0.0006 = - 16.2701 = 16.4125 = 0.0717 + 16.3549 i = 0.0717 - 16.3549 i$

Explanation

Polynomial $42 x^{6} - 12 x^{5} + 20 x^{4} + 8 x^{3} - 3000000 x^{2} + 18 x + 1$ 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)=42x6−12x5+20x4+8x3−3000000x2+18x+1

The roots of polynomial p(x) are: x1​x2​x3​x4​x5​x6​​=−0.0006=0.0006=−16.2701=16.4125=0.0717+16.3549i=0.0717−16.3549i​

Find roots of polynomial $p (x) = 42 x^{6} - 12 x^{5} + 20 x^{4} + 8 x^{3} - 3000000 x^{2} + 18 x + 1$

The roots of polynomial $p (x)$ are:
$x_{1} x_{2} x_{3} x_{4} x_{5} x_{6} = - 0.0006 = 0.0006 = - 16.2701 = 16.4125 = 0.0717 + 16.3549 i = 0.0717 - 16.3549 i$