What are the solutions to the equation 5x^4+2x^3-1=0 ?

The solutions to the equation 5x^4+2x^3-1=0 are x\approx 0.58730…,x\approx-0.79621…

Find the zeros of 5x^4+2x^3-1=0

The zeros of 5x^4+2x^3-1=0 are x\approx 0.58730…,x\approx-0.79621…

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5 x^{4} + 2 x^{3} - 1 = 0

x \approx 0.58730 \dots, x \approx - 0.79621 \dots

Solution steps

5 x^{4} + 2 x^{3} - 1 = 0

Find one solution for

5 x^{4} + 2 x^{3} - 1 = 0

using Newton-Raphson:

x \approx 0.58730 \dots

Apply long division:

\frac{5 x ^{4} + 2 x ^{3} - 1}{x - 0.58730 \dots} = 5 x^{3} + 4.93650 \dots x^{2} + 2.89920 \dots x + 1.70270 \dots

5 x^{3} + 4.93650 \dots x^{2} + 2.89920 \dots x + 1.70270 \dots \approx 0

Find one solution for

5 x^{3} + 4.93650 \dots x^{2} + 2.89920 \dots x + 1.70270 \dots = 0

using Newton-Raphson:

x \approx - 0.79621 \dots

Apply long division:

\frac{5 x ^{3} + 4.93650 \dots x ^{2} + 2.89920 \dots x + 1.70270 \dots}{x + 0.79621 \dots} = 5 x^{2} + 0.95541 \dots x + 2.13849 \dots

5 x^{2} + 0.95541 \dots x + 2.13849 \dots \approx 0

Find one solution for

5 x^{2} + 0.95541 \dots x + 2.13849 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.58730 \dots, x \approx - 0.79621 \dots

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

x^{3} = 7

15 t^{3} - 70 t^{2} + 40 t = 0

28 a^{12} = 56 a^{15}

\frac{x ^{13}}{3 ^{7}} = 3^{6}

What are the solutions to the equation 5x^4+2x^3-1=0 ?
The solutions to the equation 5x^4+2x^3-1=0 are x\approx 0.58730…,x\approx-0.79621…
Find the zeros of 5x^4+2x^3-1=0
The zeros of 5x^4+2x^3-1=0 are x\approx 0.58730…,x\approx-0.79621…