What are the solutions to the equation x^3-9x+5=0 ?

The solutions to the equation x^3-9x+5=0 are x\approx 0.57688…,x\approx 2.66966…,x\approx-3.24655…

Find the zeros of x^3-9x+5=0

The zeros of x^3-9x+5=0 are x\approx 0.57688…,x\approx 2.66966…,x\approx-3.24655…

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x^{3} - 9 x + 5 = 0

x \approx 0.57688 \dots, x \approx 2.66966 \dots, x \approx - 3.24655 \dots

Solution steps

x^{3} - 9 x + 5 = 0

Find one solution for

x^{3} - 9 x + 5 = 0

using Newton-Raphson:

x \approx 0.57688 \dots

Apply long division:

\frac{x ^{3} - 9 x + 5}{x - 0.57688 \dots} = x^{2} + 0.57688 \dots x - 8.66720 \dots

x^{2} + 0.57688 \dots x - 8.66720 \dots \approx 0

Find one solution for

x^{2} + 0.57688 \dots x - 8.66720 \dots = 0

using Newton-Raphson:

x \approx 2.66966 \dots

Apply long division:

\frac{x ^{2} + 0.57688 \dots x - 8.66720 \dots}{x - 2.66966 \dots} = x + 3.24655 \dots

x + 3.24655 \dots \approx 0

x \approx - 3.24655 \dots

The solutions are

x \approx 0.57688 \dots, x \approx 2.66966 \dots, x \approx - 3.24655 \dots

x^{4} + 4 x^{3} + x^{2} + 2 x + 2 = 0

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

x (x + 1) (x^{2} - 36) = 0

x^{3} - 3 x^{2} - 50 = 0

72 x^{4} - x^{2} - 1 = 0

What are the solutions to the equation x^3-9x+5=0 ?
The solutions to the equation x^3-9x+5=0 are x\approx 0.57688…,x\approx 2.66966…,x\approx-3.24655…
Find the zeros of x^3-9x+5=0
The zeros of x^3-9x+5=0 are x\approx 0.57688…,x\approx 2.66966…,x\approx-3.24655…