What are the solutions to the equation 0=2x^{(3)}+x^{(2)}+2x-1 ?

The solutions to the equation 0=2x^{(3)}+x^{(2)}+2x-1 are x\approx 0.37608…

Find the zeros of 0=2x^{(3)}+x^{(2)}+2x-1

The zeros of 0=2x^{(3)}+x^{(2)}+2x-1 are x\approx 0.37608…

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

x \approx 0.37608 \dots

Solution steps

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

Refine

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

Switch sides

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.37608 \dots

Apply long division:

\frac{2 x ^{3} + x ^{2} + 2 x - 1}{x - 0.37608 \dots} = 2 x^{2} + 1.75217 \dots x + 2.65896 \dots

2 x^{2} + 1.75217 \dots x + 2.65896 \dots \approx 0

Find one solution for

2 x^{2} + 1.75217 \dots x + 2.65896 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.37608 \dots

m^{3} = 125

5 x^{3} - 3 x - 1 = 0

16 x^{4} = 1048576

- (a + 1)^{2} (a - 8) = 0

x^{2} + 6 x + 9 = 4 x^{4}

What are the solutions to the equation 0=2x^{(3)}+x^{(2)}+2x-1 ?
The solutions to the equation 0=2x^{(3)}+x^{(2)}+2x-1 are x\approx 0.37608…
Find the zeros of 0=2x^{(3)}+x^{(2)}+2x-1
The zeros of 0=2x^{(3)}+x^{(2)}+2x-1 are x\approx 0.37608…