What are the solutions to the equation 2a^3-2a^2+1=0 ?

The solutions to the equation 2a^3-2a^2+1=0 are a\approx-0.56519…

Find the zeros of 2a^3-2a^2+1=0

The zeros of 2a^3-2a^2+1=0 are a\approx-0.56519…

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

a \approx - 0.56519 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

a \approx - 0.56519 \dots

Apply long division:

\frac{2 a ^{3} - 2 a ^{2} + 1}{a + 0.56519 \dots} = 2 a^{2} - 3.13039 \dots a + 1.76929 \dots

2 a^{2} - 3.13039 \dots a + 1.76929 \dots \approx 0

Find one solution for

2 a^{2} - 3.13039 \dots a + 1.76929 \dots = 0

using Newton-Raphson:

No Solution for

a \in R

The solution is

a \approx - 0.56519 \dots

(4 x^{2} + 1)^{2} = 0

45 = 30 (1 + x)^{3}

60 x^{4} - 180 x^{3} + 120 x^{2} = 0

x (x + 2) (x - 3) + 3 = 0

x^{3} - 16 x^{2} + 64 x = 0

What are the solutions to the equation 2a^3-2a^2+1=0 ?
The solutions to the equation 2a^3-2a^2+1=0 are a\approx-0.56519…
Find the zeros of 2a^3-2a^2+1=0
The zeros of 2a^3-2a^2+1=0 are a\approx-0.56519…