What are the solutions to the equation x^4-5x^2+6x-4=0 ?

The solutions to the equation x^4-5x^2+6x-4=0 are x\approx-2.77216…,x\approx 1.68799…

Find the zeros of x^4-5x^2+6x-4=0

The zeros of x^4-5x^2+6x-4=0 are x\approx-2.77216…,x\approx 1.68799…

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x^{4} - 5 x^{2} + 6 x - 4 = 0

x \approx - 2.77216 \dots, x \approx 1.68799 \dots

Solution steps

x^{4} - 5 x^{2} + 6 x - 4 = 0

Find one solution for

x^{4} - 5 x^{2} + 6 x - 4 = 0

using Newton-Raphson:

x \approx - 2.77216 \dots

Apply long division:

\frac{x ^{4} - 5 x ^{2} + 6 x - 4}{x + 2.77216 \dots} = x^{3} - 2.77216 \dots x^{2} + 2.68487 \dots x - 1.44291 \dots

x^{3} - 2.77216 \dots x^{2} + 2.68487 \dots x - 1.44291 \dots \approx 0

Find one solution for

x^{3} - 2.77216 \dots x^{2} + 2.68487 \dots x - 1.44291 \dots = 0

using Newton-Raphson:

x \approx 1.68799 \dots

Apply long division:

\frac{x ^{3} - 2.77216 \dots x ^{2} + 2.68487 \dots x - 1.44291 \dots}{x - 1.68799 \dots} = x^{2} - 1.08416 \dots x + 0.85481 \dots

x^{2} - 1.08416 \dots x + 0.85481 \dots \approx 0

Find one solution for

x^{2} - 1.08416 \dots x + 0.85481 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 2.77216 \dots, x \approx 1.68799 \dots

5 x^{4} = 80

n^{3} - 3 n = 40

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

y, x = y^{4} - 16

0 = 10 x^{3} + 19 x^{2} - 5 x - 6

What are the solutions to the equation x^4-5x^2+6x-4=0 ?
The solutions to the equation x^4-5x^2+6x-4=0 are x\approx-2.77216…,x\approx 1.68799…
Find the zeros of x^4-5x^2+6x-4=0
The zeros of x^4-5x^2+6x-4=0 are x\approx-2.77216…,x\approx 1.68799…