What are the solutions to the equation x^4-12x^2+16sqrt(2)x-12=0 ?

The solutions to the equation x^4-12x^2+16sqrt(2)x-12=0 are x\approx-4.24264…,x\approx 1.41432…

Find the zeros of x^4-12x^2+16sqrt(2)x-12=0

The zeros of x^4-12x^2+16sqrt(2)x-12=0 are x\approx-4.24264…,x\approx 1.41432…

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x^{4} - 12 x^{2} + 162 x - 12 = 0

x \approx - 4.24264 \dots, x \approx 1.41432 \dots

Solution steps

x^{4} - 12 x^{2} + 162 x - 12 = 0

Find one solution for

x^{4} - 12 x^{2} + 22.62741 \dots x - 12 = 0

using Newton-Raphson:

x \approx - 4.24264 \dots

Apply long division:

\frac{x ^{4} - 12 x ^{2} + 16 2 x - 12}{x + 4.24264 \dots} = x^{3} - 4.24264 \dots x^{2} + 6 x - 2.82842 \dots

x^{3} - 4.24264 \dots x^{2} + 6 x - 2.82842 \dots \approx 0

Find one solution for

x^{3} - 4.24264 \dots x^{2} + 6 x - 2.82842 \dots = 0

using Newton-Raphson:

x \approx 1.41432 \dots

Apply long division:

\frac{x ^{3} - 4.24264 \dots x ^{2} + 6 x - 2.82842 \dots}{x - 1.41432 \dots} = x^{2} - 2.82831 \dots x + 1.99984 \dots

x^{2} - 2.82831 \dots x + 1.99984 \dots \approx 0

Find one solution for

x^{2} - 2.82831 \dots x + 1.99984 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 4.24264 \dots, x \approx 1.41432 \dots

x^{4} + 8 x^{3} + 16 x^{2} = 0

x^{4} + 130 x^{2} + 3969 = 0

81 x^{3} = x^{2}

3 m^{3} + 12 m^{2} - 135 m = 0

x^{4} - 6 x^{2} + 20 x - 24 = 0

What are the solutions to the equation x^4-12x^2+16sqrt(2)x-12=0 ?
The solutions to the equation x^4-12x^2+16sqrt(2)x-12=0 are x\approx-4.24264…,x\approx 1.41432…
Find the zeros of x^4-12x^2+16sqrt(2)x-12=0
The zeros of x^4-12x^2+16sqrt(2)x-12=0 are x\approx-4.24264…,x\approx 1.41432…