What are the solutions to the equation x^5-80x+50=0 ?

The solutions to the equation x^5-80x+50=0 are x\approx 0.62620…,x\approx 2.80827…,x\approx-3.12996…

Find the zeros of x^5-80x+50=0

The zeros of x^5-80x+50=0 are x\approx 0.62620…,x\approx 2.80827…,x\approx-3.12996…

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x^{5} - 80 x + 50 = 0

x \approx 0.62620 \dots, x \approx 2.80827 \dots, x \approx - 3.12996 \dots

Solution steps

x^{5} - 80 x + 50 = 0

Find one solution for

x^{5} - 80 x + 50 = 0

using Newton-Raphson:

x \approx 0.62620 \dots

Apply long division:

\frac{x ^{5} - 80 x + 50}{x - 0.62620 \dots} = x^{4} + 0.62620 \dots x^{3} + 0.39213 \dots x^{2} + 0.24555 \dots x - 79.84623 \dots

x^{4} + 0.62620 \dots x^{3} + 0.39213 \dots x^{2} + 0.24555 \dots x - 79.84623 \dots \approx 0

Find one solution for

x^{4} + 0.62620 \dots x^{3} + 0.39213 \dots x^{2} + 0.24555 \dots x - 79.84623 \dots = 0

using Newton-Raphson:

x \approx 2.80827 \dots

Apply long division:

\frac{x ^{4} + 0.62620 \dots x ^{3} + 0.39213 \dots x ^{2} + 0.24555 \dots x - 79.84623 \dots}{x - 2.80827 \dots} = x^{3} + 3.43447 \dots x^{2} + 10.03709 \dots x + 28.43247 \dots

x^{3} + 3.43447 \dots x^{2} + 10.03709 \dots x + 28.43247 \dots \approx 0

Find one solution for

x^{3} + 3.43447 \dots x^{2} + 10.03709 \dots x + 28.43247 \dots = 0

using Newton-Raphson:

x \approx - 3.12996 \dots

Apply long division:

\frac{x ^{3} + 3.43447 \dots x ^{2} + 10.03709 \dots x + 28.43247 \dots}{x + 3.12996 \dots} = x^{2} + 0.30451 \dots x + 9.08396 \dots

x^{2} + 0.30451 \dots x + 9.08396 \dots \approx 0

Find one solution for

x^{2} + 0.30451 \dots x + 9.08396 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.62620 \dots, x \approx 2.80827 \dots, x \approx - 3.12996 \dots

8 x^{5} - 4 x^{3} + 2 = 0

w^{3} - 2 w^{2} + w - 2 = 0.2

- 4 x^{5} + 32 x^{3} + 192 x = 0

- 2 x^{3} - x^{2} + 8 x - 5 = 0

(x^{3}) (x + 3) = 5

What are the solutions to the equation x^5-80x+50=0 ?
The solutions to the equation x^5-80x+50=0 are x\approx 0.62620…,x\approx 2.80827…,x\approx-3.12996…
Find the zeros of x^5-80x+50=0
The zeros of x^5-80x+50=0 are x\approx 0.62620…,x\approx 2.80827…,x\approx-3.12996…