What are the solutions to the equation x^4-13x^3+36=0 ?

The solutions to the equation x^4-13x^3+36=0 are x\approx 12.98355…,x\approx 1.46121…

Find the zeros of x^4-13x^3+36=0

The zeros of x^4-13x^3+36=0 are x\approx 12.98355…,x\approx 1.46121…

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x^{4} - 13 x^{3} + 36 = 0

x \approx 12.98355 \dots, x \approx 1.46121 \dots

Solution steps

x^{4} - 13 x^{3} + 36 = 0

Find one solution for

x^{4} - 13 x^{3} + 36 = 0

using Newton-Raphson:

x \approx 12.98355 \dots

Apply long division:

\frac{x ^{4} - 13 x ^{3} + 36}{x - 12.98355 \dots} = x^{3} - 0.01644 \dots x^{2} - 0.21355 \dots x - 2.77273 \dots

x^{3} - 0.01644 \dots x^{2} - 0.21355 \dots x - 2.77273 \dots \approx 0

Find one solution for

x^{3} - 0.01644 \dots x^{2} - 0.21355 \dots x - 2.77273 \dots = 0

using Newton-Raphson:

x \approx 1.46121 \dots

Apply long division:

\frac{x ^{3} - 0.01644 \dots x ^{2} - 0.21355 \dots x - 2.77273 \dots}{x - 1.46121 \dots} = x^{2} + 1.44476 \dots x + 1.89755 \dots

x^{2} + 1.44476 \dots x + 1.89755 \dots \approx 0

Find one solution for

x^{2} + 1.44476 \dots x + 1.89755 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 12.98355 \dots, x \approx 1.46121 \dots

x^{4} - 7 x^{3} + 15 x^{2} - 9 x = 0

6 x^{3} + 4 x^{2} = 10 x

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

6 p + 2 = p^{2} + 3 p^{3}

n, A = 2 r h + 2 s n^{3}

What are the solutions to the equation x^4-13x^3+36=0 ?
The solutions to the equation x^4-13x^3+36=0 are x\approx 12.98355…,x\approx 1.46121…
Find the zeros of x^4-13x^3+36=0
The zeros of x^4-13x^3+36=0 are x\approx 12.98355…,x\approx 1.46121…