What are the solutions to the equation 4x^5-5x^4+5x^3+11x^2-24x+12=0 ?

The solutions to the equation 4x^5-5x^4+5x^3+11x^2-24x+12=0 are x\approx-1.50128…

Find the zeros of 4x^5-5x^4+5x^3+11x^2-24x+12=0

The zeros of 4x^5-5x^4+5x^3+11x^2-24x+12=0 are x\approx-1.50128…

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4 x^{5} - 5 x^{4} + 5 x^{3} + 11 x^{2} - 24 x + 12 = 0

x \approx - 1.50128 \dots

Solution steps

4 x^{5} - 5 x^{4} + 5 x^{3} + 11 x^{2} - 24 x + 12 = 0

Find one solution for

4 x^{5} - 5 x^{4} + 5 x^{3} + 11 x^{2} - 24 x + 12 = 0

using Newton-Raphson:

x \approx - 1.50128 \dots

Apply long division:

\frac{4 x ^{5} - 5 x ^{4} + 5 x ^{3} + 11 x ^{2} - 24 x + 12}{x + 1.50128 \dots} = 4 x^{4} - 11.00514 \dots x^{3} + 21.52187 \dots x^{2} - 21.31049 \dots x + 7.99314 \dots

4 x^{4} - 11.00514 \dots x^{3} + 21.52187 \dots x^{2} - 21.31049 \dots x + 7.99314 \dots \approx 0

Find one solution for

4 x^{4} - 11.00514 \dots x^{3} + 21.52187 \dots x^{2} - 21.31049 \dots x + 7.99314 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 1.50128 \dots

y, x^{4} + y^{4} = x^{2} y^{2}

x^{3} + 6 x^{2} + 8 x + 10

2 x^{3} - 6 x^{2} - 3 x - 10 = 0

z^{3} - 8 i = 0

3 x^{3} + 7 x^{2} + 6 x - 8 = 0

What are the solutions to the equation 4x^5-5x^4+5x^3+11x^2-24x+12=0 ?
The solutions to the equation 4x^5-5x^4+5x^3+11x^2-24x+12=0 are x\approx-1.50128…
Find the zeros of 4x^5-5x^4+5x^3+11x^2-24x+12=0
The zeros of 4x^5-5x^4+5x^3+11x^2-24x+12=0 are x\approx-1.50128…