What are the solutions to the equation x^4-10x^2-3x+25=0 ?

The solutions to the equation x^4-10x^2-3x+25=0 are x\approx 2.81143…,x\approx 1.66320…

Find the zeros of x^4-10x^2-3x+25=0

The zeros of x^4-10x^2-3x+25=0 are x\approx 2.81143…,x\approx 1.66320…

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x^{4} - 10 x^{2} - 3 x + 25 = 0

x \approx 2.81143 \dots, x \approx 1.66320 \dots

Solution steps

x^{4} - 10 x^{2} - 3 x + 25 = 0

Find one solution for

x^{4} - 10 x^{2} - 3 x + 25 = 0

using Newton-Raphson:

x \approx 2.81143 \dots

Apply long division:

\frac{x ^{4} - 10 x ^{2} - 3 x + 25}{x - 2.81143 \dots} = x^{3} + 2.81143 \dots x^{2} - 2.09581 \dots x - 8.89224 \dots

x^{3} + 2.81143 \dots x^{2} - 2.09581 \dots x - 8.89224 \dots \approx 0

Find one solution for

x^{3} + 2.81143 \dots x^{2} - 2.09581 \dots x - 8.89224 \dots = 0

using Newton-Raphson:

x \approx 1.66320 \dots

Apply long division:

\frac{x ^{3} + 2.81143 \dots x ^{2} - 2.09581 \dots x - 8.89224 \dots}{x - 1.66320 \dots} = x^{2} + 4.47464 \dots x + 5.34644 \dots

x^{2} + 4.47464 \dots x + 5.34644 \dots \approx 0

Find one solution for

x^{2} + 4.47464 \dots x + 5.34644 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 2.81143 \dots, x \approx 1.66320 \dots

x^{4} - 11 x^{2} + 24 = 0

x^{4} = \frac{1}{80}

x^{3} - 10 x^{2} = 0

3900 + 503.13 = 3900 - (1 - x)^{3}

- 6 x^{3} = 0

What are the solutions to the equation x^4-10x^2-3x+25=0 ?
The solutions to the equation x^4-10x^2-3x+25=0 are x\approx 2.81143…,x\approx 1.66320…
Find the zeros of x^4-10x^2-3x+25=0
The zeros of x^4-10x^2-3x+25=0 are x\approx 2.81143…,x\approx 1.66320…