What are the solutions to the equation x^4-4x^3-4x^2-10=0 ?

The solutions to the equation x^4-4x^3-4x^2-10=0 are x\approx 4.90108…,x\approx-1.51512…

Find the zeros of x^4-4x^3-4x^2-10=0

The zeros of x^4-4x^3-4x^2-10=0 are x\approx 4.90108…,x\approx-1.51512…

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x^{4} - 4 x^{3} - 4 x^{2} - 10 = 0

x \approx 4.90108 \dots, x \approx - 1.51512 \dots

Solution steps

x^{4} - 4 x^{3} - 4 x^{2} - 10 = 0

Find one solution for

x^{4} - 4 x^{3} - 4 x^{2} - 10 = 0

using Newton-Raphson:

x \approx 4.90108 \dots

Apply long division:

\frac{x ^{4} - 4 x ^{3} - 4 x ^{2} - 10}{x - 4.90108 \dots} = x^{3} + 0.90108 \dots x^{2} + 0.41630 \dots x + 2.04036 \dots

x^{3} + 0.90108 \dots x^{2} + 0.41630 \dots x + 2.04036 \dots \approx 0

Find one solution for

x^{3} + 0.90108 \dots x^{2} + 0.41630 \dots x + 2.04036 \dots = 0

using Newton-Raphson:

x \approx - 1.51512 \dots

Apply long division:

\frac{x ^{3} + 0.90108 \dots x ^{2} + 0.41630 \dots x + 2.04036 \dots}{x + 1.51512 \dots} = x^{2} - 0.61404 \dots x + 1.34666 \dots

x^{2} - 0.61404 \dots x + 1.34666 \dots \approx 0

Find one solution for

x^{2} - 0.61404 \dots x + 1.34666 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 4.90108 \dots, x \approx - 1.51512 \dots

x^{4} - 8 x^{2} + x + 12 = 0

z^{3} + z^{2} + z + 1 = 0

(2 x - 1)^{4} - 16 = 0

(x - 5)^{3} = 0

12 x^{5} = (4 x^{2}) (c)

What are the solutions to the equation x^4-4x^3-4x^2-10=0 ?
The solutions to the equation x^4-4x^3-4x^2-10=0 are x\approx 4.90108…,x\approx-1.51512…
Find the zeros of x^4-4x^3-4x^2-10=0
The zeros of x^4-4x^3-4x^2-10=0 are x\approx 4.90108…,x\approx-1.51512…