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

The solutions to the equation 5y^4-y^2+2y-4=0 are y\approx 0.88114…,y\approx-1.10396…

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

The zeros of 5y^4-y^2+2y-4=0 are y\approx 0.88114…,y\approx-1.10396…

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5 y^{4} - y^{2} + 2 y - 4 = 0

y \approx 0.88114 \dots, y \approx - 1.10396 \dots

Solution steps

5 y^{4} - y^{2} + 2 y - 4 = 0

Find one solution for

5 y^{4} - y^{2} + 2 y - 4 = 0

using Newton-Raphson:

y \approx 0.88114 \dots

Apply long division:

\frac{5 y ^{4} - y ^{2} + 2 y - 4}{y - 0.88114 \dots} = 5 y^{3} + 4.40572 \dots y^{2} + 2.88209 \dots y + 4.53954 \dots

5 y^{3} + 4.40572 \dots y^{2} + 2.88209 \dots y + 4.53954 \dots \approx 0

Find one solution for

5 y^{3} + 4.40572 \dots y^{2} + 2.88209 \dots y + 4.53954 \dots = 0

using Newton-Raphson:

y \approx - 1.10396 \dots

Apply long division:

\frac{5 y ^{3} + 4.40572 \dots y ^{2} + 2.88209 \dots y + 4.53954 \dots}{y + 1.10396 \dots} = 5 y^{2} - 1.11410 \dots y + 4.11202 \dots

5 y^{2} - 1.11410 \dots y + 4.11202 \dots \approx 0

Find one solution for

5 y^{2} - 1.11410 \dots y + 4.11202 \dots = 0

using Newton-Raphson:

No Solution for

y \in R

The solutions are

y \approx 0.88114 \dots, y \approx - 1.10396 \dots

x^{4} - 2 x^{2} + 1

4 x^{3} - 9 x^{2} - 1 = \frac{1}{2}

10 x^{9} - 9 x^{10} = 0.75

(2 z - i)^{3} = 33

(2 x - 1) (x^{2} + 2 x + 1) = 2 x^{2} + 2 x

What are the solutions to the equation 5y^4-y^2+2y-4=0 ?
The solutions to the equation 5y^4-y^2+2y-4=0 are y\approx 0.88114…,y\approx-1.10396…
Find the zeros of 5y^4-y^2+2y-4=0
The zeros of 5y^4-y^2+2y-4=0 are y\approx 0.88114…,y\approx-1.10396…