What are the solutions to the equation 15x^4-8x^3+54x^2+18x-4=0 ?

The solutions to the equation 15x^4-8x^3+54x^2+18x-4=0 are x\approx 0.15306…,x\approx-0.44558…

Find the zeros of 15x^4-8x^3+54x^2+18x-4=0

The zeros of 15x^4-8x^3+54x^2+18x-4=0 are x\approx 0.15306…,x\approx-0.44558…

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15 x^{4} - 8 x^{3} + 54 x^{2} + 18 x - 4 = 0

x \approx 0.15306 \dots, x \approx - 0.44558 \dots

Solution steps

15 x^{4} - 8 x^{3} + 54 x^{2} + 18 x - 4 = 0

Find one solution for

15 x^{4} - 8 x^{3} + 54 x^{2} + 18 x - 4 = 0

using Newton-Raphson:

x \approx 0.15306 \dots

Apply long division:

\frac{15 x ^{4} - 8 x ^{3} + 54 x ^{2} + 18 x - 4}{x - 0.15306 \dots} = 15 x^{3} - 5.70397 \dots x^{2} + 53.12690 \dots x + 26.13206 \dots

15 x^{3} - 5.70397 \dots x^{2} + 53.12690 \dots x + 26.13206 \dots \approx 0

Find one solution for

15 x^{3} - 5.70397 \dots x^{2} + 53.12690 \dots x + 26.13206 \dots = 0

using Newton-Raphson:

x \approx - 0.44558 \dots

Apply long division:

\frac{15 x ^{3} - 5.70397 \dots x ^{2} + 53.12690 \dots x + 26.13206 \dots}{x + 0.44558 \dots} = 15 x^{2} - 12.38773 \dots x + 58.64668 \dots

15 x^{2} - 12.38773 \dots x + 58.64668 \dots \approx 0

Find one solution for

15 x^{2} - 12.38773 \dots x + 58.64668 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.15306 \dots, x \approx - 0.44558 \dots

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

x^{2} + x^{3} = 5

x^{4} - x^{2} = 2

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

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

What are the solutions to the equation 15x^4-8x^3+54x^2+18x-4=0 ?
The solutions to the equation 15x^4-8x^3+54x^2+18x-4=0 are x\approx 0.15306…,x\approx-0.44558…
Find the zeros of 15x^4-8x^3+54x^2+18x-4=0
The zeros of 15x^4-8x^3+54x^2+18x-4=0 are x\approx 0.15306…,x\approx-0.44558…