What are the solutions to the equation 3x^4+4x^3+6x^2-4=0 ?

The solutions to the equation 3x^4+4x^3+6x^2-4=0 are x\approx 0.63939…,x\approx-0.90884…

Find the zeros of 3x^4+4x^3+6x^2-4=0

The zeros of 3x^4+4x^3+6x^2-4=0 are x\approx 0.63939…,x\approx-0.90884…

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3 x^{4} + 4 x^{3} + 6 x^{2} - 4 = 0

x \approx 0.63939 \dots, x \approx - 0.90884 \dots

Solution steps

3 x^{4} + 4 x^{3} + 6 x^{2} - 4 = 0

Find one solution for

3 x^{4} + 4 x^{3} + 6 x^{2} - 4 = 0

using Newton-Raphson:

x \approx 0.63939 \dots

Apply long division:

\frac{3 x ^{4} + 4 x ^{3} + 6 x ^{2} - 4}{x - 0.63939 \dots} = 3 x^{3} + 5.91818 \dots x^{2} + 9.78406 \dots x + 6.25589 \dots

3 x^{3} + 5.91818 \dots x^{2} + 9.78406 \dots x + 6.25589 \dots \approx 0

Find one solution for

3 x^{3} + 5.91818 \dots x^{2} + 9.78406 \dots x + 6.25589 \dots = 0

using Newton-Raphson:

x \approx - 0.90884 \dots

Apply long division:

\frac{3 x ^{3} + 5.91818 \dots x ^{2} + 9.78406 \dots x + 6.25589 \dots}{x + 0.90884 \dots} = 3 x^{2} + 3.19165 \dots x + 6.88335 \dots

3 x^{2} + 3.19165 \dots x + 6.88335 \dots \approx 0

Find one solution for

3 x^{2} + 3.19165 \dots x + 6.88335 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.63939 \dots, x \approx - 0.90884 \dots

x^{3} - 2 x = 88

- 32 x^{5} + 160 x^{3} - 120 x = 0

s^{4} - 10 s^{3} - 5 s^{2} = 0

x, x^{4} - 81 = 0

v^{10} - 6 v = - 104

What are the solutions to the equation 3x^4+4x^3+6x^2-4=0 ?
The solutions to the equation 3x^4+4x^3+6x^2-4=0 are x\approx 0.63939…,x\approx-0.90884…
Find the zeros of 3x^4+4x^3+6x^2-4=0
The zeros of 3x^4+4x^3+6x^2-4=0 are x\approx 0.63939…,x\approx-0.90884…