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

The solutions to the equation x^4-4x^2-3x+5=0 are x\approx 2.06932…,x\approx 0.86117…

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

The zeros of x^4-4x^2-3x+5=0 are x\approx 2.06932…,x\approx 0.86117…

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

x \approx 2.06932 \dots, x \approx 0.86117 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 2.06932 \dots

Apply long division:

\frac{x ^{4} - 4 x ^{2} - 3 x + 5}{x - 2.06932 \dots} = x^{3} + 2.06932 \dots x^{2} + 0.28209 \dots x - 2.41624 \dots

x^{3} + 2.06932 \dots x^{2} + 0.28209 \dots x - 2.41624 \dots \approx 0

Find one solution for

x^{3} + 2.06932 \dots x^{2} + 0.28209 \dots x - 2.41624 \dots = 0

using Newton-Raphson:

x \approx 0.86117 \dots

Apply long division:

\frac{x ^{3} + 2.06932 \dots x ^{2} + 0.28209 \dots x - 2.41624 \dots}{x - 0.86117 \dots} = x^{2} + 2.93049 \dots x + 2.80576 \dots

x^{2} + 2.93049 \dots x + 2.80576 \dots \approx 0

Find one solution for

x^{2} + 2.93049 \dots x + 2.80576 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 2.06932 \dots, x \approx 0.86117 \dots

\frac{x ^{4}}{8 + 1} = 33

x^{4} + 4 x^{3} + 3 x^{2} - 4 x - 4 = 0

x^{6} + 2 x^{3} + 1 = 0

2 x^{4} - 26 x^{2} + 72 = 0

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

What are the solutions to the equation x^4-4x^2-3x+5=0 ?
The solutions to the equation x^4-4x^2-3x+5=0 are x\approx 2.06932…,x\approx 0.86117…
Find the zeros of x^4-4x^2-3x+5=0
The zeros of x^4-4x^2-3x+5=0 are x\approx 2.06932…,x\approx 0.86117…