What are the solutions to the equation 0=x^4-4x^3+7 ?

The solutions to the equation 0=x^4-4x^3+7 are x\approx 3.88017…,x\approx 1.38923…

Find the zeros of 0=x^4-4x^3+7

The zeros of 0=x^4-4x^3+7 are x\approx 3.88017…,x\approx 1.38923…

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0 = x^{4} - 4 x^{3} + 7

x \approx 3.88017 \dots, x \approx 1.38923 \dots

Solution steps

0 = x^{4} - 4 x^{3} + 7

Switch sides

x^{4} - 4 x^{3} + 7 = 0

Find one solution for

x^{4} - 4 x^{3} + 7 = 0

using Newton-Raphson:

x \approx 3.88017 \dots

Apply long division:

\frac{x ^{4} - 4 x ^{3} + 7}{x - 3.88017 \dots} = x^{3} - 0.11982 \dots x^{2} - 0.46493 \dots x - 1.80404 \dots

x^{3} - 0.11982 \dots x^{2} - 0.46493 \dots x - 1.80404 \dots \approx 0

Find one solution for

x^{3} - 0.11982 \dots x^{2} - 0.46493 \dots x - 1.80404 \dots = 0

using Newton-Raphson:

x \approx 1.38923 \dots

Apply long division:

\frac{x ^{3} - 0.11982 \dots x ^{2} - 0.46493 \dots x - 1.80404 \dots}{x - 1.38923 \dots} = x^{2} + 1.26941 \dots x + 1.29858 \dots

x^{2} + 1.26941 \dots x + 1.29858 \dots \approx 0

Find one solution for

x^{2} + 1.26941 \dots x + 1.29858 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 3.88017 \dots, x \approx 1.38923 \dots

x^{3} - 9 x - 5 = 0

x^{3} - 7 x = 0

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

x (x - 3) (x - 1) (x + 2) = 16

(z + 3)^{4} = - 324

What are the solutions to the equation 0=x^4-4x^3+7 ?
The solutions to the equation 0=x^4-4x^3+7 are x\approx 3.88017…,x\approx 1.38923…
Find the zeros of 0=x^4-4x^3+7
The zeros of 0=x^4-4x^3+7 are x\approx 3.88017…,x\approx 1.38923…