What are the solutions to the equation 4x^3-9x+2=0 ?

The solutions to the equation 4x^3-9x+2=0 are x\approx 0.22745…,x\approx 1.37328…,x\approx-1.60073…

Find the zeros of 4x^3-9x+2=0

The zeros of 4x^3-9x+2=0 are x\approx 0.22745…,x\approx 1.37328…,x\approx-1.60073…

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4 x^{3} - 9 x + 2 = 0

x \approx 0.22745 \dots, x \approx 1.37328 \dots, x \approx - 1.60073 \dots

Solution steps

4 x^{3} - 9 x + 2 = 0

Find one solution for

4 x^{3} - 9 x + 2 = 0

using Newton-Raphson:

x \approx 0.22745 \dots

Apply long division:

\frac{4 x ^{3} - 9 x + 2}{x - 0.22745 \dots} = 4 x^{2} + 0.90980 \dots x - 8.79306 \dots

4 x^{2} + 0.90980 \dots x - 8.79306 \dots \approx 0

Find one solution for

4 x^{2} + 0.90980 \dots x - 8.79306 \dots = 0

using Newton-Raphson:

x \approx 1.37328 \dots

Apply long division:

\frac{4 x ^{2} + 0.90980 \dots x - 8.79306 \dots}{x - 1.37328 \dots} = 4 x + 6.40294 \dots

4 x + 6.40294 \dots \approx 0

x \approx - 1.60073 \dots

The solutions are

x \approx 0.22745 \dots, x \approx 1.37328 \dots, x \approx - 1.60073 \dots

4 x^{3} + 4 x^{2} - 9 x - 9 = 0

x^{3} - 2 x^{2} + x - 1 = 0

x^{4} - 6 x^{2} + 4 = 0

(x^{4} - 4) = 0

y + y^{3} = 2

What are the solutions to the equation 4x^3-9x+2=0 ?
The solutions to the equation 4x^3-9x+2=0 are x\approx 0.22745…,x\approx 1.37328…,x\approx-1.60073…
Find the zeros of 4x^3-9x+2=0
The zeros of 4x^3-9x+2=0 are x\approx 0.22745…,x\approx 1.37328…,x\approx-1.60073…