What are the solutions to the equation 3x^4-x^3+4x^2-5=0 ?

The solutions to the equation 3x^4-x^3+4x^2-5=0 are x\approx 0.93688…,x\approx-0.84568…

Find the zeros of 3x^4-x^3+4x^2-5=0

The zeros of 3x^4-x^3+4x^2-5=0 are x\approx 0.93688…,x\approx-0.84568…

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

x \approx 0.93688 \dots, x \approx - 0.84568 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.93688 \dots

Apply long division:

\frac{3 x ^{4} - x ^{3} + 4 x ^{2} - 5}{x - 0.93688 \dots} = 3 x^{3} + 1.81065 \dots x^{2} + 5.69637 \dots x + 5.33683 \dots

3 x^{3} + 1.81065 \dots x^{2} + 5.69637 \dots x + 5.33683 \dots \approx 0

Find one solution for

3 x^{3} + 1.81065 \dots x^{2} + 5.69637 \dots x + 5.33683 \dots = 0

using Newton-Raphson:

x \approx - 0.84568 \dots

Apply long division:

\frac{3 x ^{3} + 1.81065 \dots x ^{2} + 5.69637 \dots x + 5.33683 \dots}{x + 0.84568 \dots} = 3 x^{2} - 0.72640 \dots x + 6.31067 \dots

3 x^{2} - 0.72640 \dots x + 6.31067 \dots \approx 0

Find one solution for

3 x^{2} - 0.72640 \dots x + 6.31067 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.93688 \dots, x \approx - 0.84568 \dots

y^{3} = 18

y^{3} = 14

y^{3} = 11

2 x ((5) 4) = ((2) 5) x^{4}

y^{3} = - 9

What are the solutions to the equation 3x^4-x^3+4x^2-5=0 ?
The solutions to the equation 3x^4-x^3+4x^2-5=0 are x\approx 0.93688…,x\approx-0.84568…
Find the zeros of 3x^4-x^3+4x^2-5=0
The zeros of 3x^4-x^3+4x^2-5=0 are x\approx 0.93688…,x\approx-0.84568…