What are the solutions to the equation roots x^7-3x^5+x^2-2x+13 ?

The solutions to the equation roots x^7-3x^5+x^2-2x+13 are x\approx-1.93779…

Find the zeros of roots x^7-3x^5+x^2-2x+13

The zeros of roots x^7-3x^5+x^2-2x+13 are x\approx-1.93779…

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roots

x^{7} - 3 x^{5} + x^{2} - 2 x + 13

x \approx - 1.93779 \dots

Solution steps

x^{7} - 3 x^{5} + x^{2} - 2 x + 13

The roots are the intercepts with the x-axis

(y = 0)

x^{7} - 3 x^{5} + x^{2} - 2 x + 13 = 0

Find one solution for

x^{7} - 3 x^{5} + x^{2} - 2 x + 13 = 0

using Newton-Raphson:

x \approx - 1.93779 \dots

Apply long division:

\frac{x ^{7} - 3 x ^{5} + x ^{2} - 2 x + 13}{x + 1.93779 \dots} = x^{6} - 1.93779 \dots x^{5} + 0.75504 \dots x^{4} - 1.46312 \dots x^{3} + 2.83523 \dots x^{2} - 4.49410 \dots x + 6.70865 \dots

x^{6} - 1.93779 \dots x^{5} + 0.75504 \dots x^{4} - 1.46312 \dots x^{3} + 2.83523 \dots x^{2} - 4.49410 \dots x + 6.70865 \dots \approx 0

Find one solution for

x^{6} - 1.93779 \dots x^{5} + 0.75504 \dots x^{4} - 1.46312 \dots x^{3} + 2.83523 \dots x^{2} - 4.49410 \dots x + 6.70865 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 1.93779 \dots

z^{4} + 6 (1 + i) z^{2} + 5 + 6 i = 0

x^{3} - 4 x^{2} + 25 x - 100 = 0

(x + 1)^{2} (x - 5) = 0

- 4 x^{3} = 32

r^{5} - r^{4} - 4 r^{3} - 4 r^{2} - 5 r - 3 = 0

What are the solutions to the equation roots x^7-3x^5+x^2-2x+13 ?
The solutions to the equation roots x^7-3x^5+x^2-2x+13 are x\approx-1.93779…
Find the zeros of roots x^7-3x^5+x^2-2x+13
The zeros of roots x^7-3x^5+x^2-2x+13 are x\approx-1.93779…