What are the solutions to the equation x^4+6*x^2-60x+36=0 ?

The solutions to the equation x^4+6*x^2-60x+36=0 are x\approx 0.64439…,x\approx 3.09987…

Find the zeros of x^4+6*x^2-60x+36=0

The zeros of x^4+6*x^2-60x+36=0 are x\approx 0.64439…,x\approx 3.09987…

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x^{4} + 6 \cdot x^{2} - 60 x + 36 = 0

x \approx 0.64439 \dots, x \approx 3.09987 \dots

Solution steps

x^{4} + 6 x^{2} - 60 x + 36 = 0

Find one solution for

x^{4} + 6 x^{2} - 60 x + 36 = 0

using Newton-Raphson:

x \approx 0.64439 \dots

Apply long division:

\frac{x ^{4} + 6 x ^{2} - 60 x + 36}{x - 0.64439 \dots} = x^{3} + 0.64439 \dots x^{2} + 6.41524 \dots x - 55.86602 \dots

x^{3} + 0.64439 \dots x^{2} + 6.41524 \dots x - 55.86602 \dots \approx 0

Find one solution for

x^{3} + 0.64439 \dots x^{2} + 6.41524 \dots x - 55.86602 \dots = 0

using Newton-Raphson:

x \approx 3.09987 \dots

Apply long division:

\frac{x ^{3} + 0.64439 \dots x ^{2} + 6.41524 \dots x - 55.86602 \dots}{x - 3.09987 \dots} = x^{2} + 3.74427 \dots x + 18.02202 \dots

x^{2} + 3.74427 \dots x + 18.02202 \dots \approx 0

Find one solution for

x^{2} + 3.74427 \dots x + 18.02202 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.64439 \dots, x \approx 3.09987 \dots

x^{4} - 6 x^{2} = 27

x (x - 3) (2 x - 1) = 0

j (x) = 3 x^{3}, [1, 1 + h (x)]

6 x^{3} - 2 = 0

27 = t^{3}

What are the solutions to the equation x^4+6*x^2-60x+36=0 ?
The solutions to the equation x^4+6*x^2-60x+36=0 are x\approx 0.64439…,x\approx 3.09987…
Find the zeros of x^4+6*x^2-60x+36=0
The zeros of x^4+6*x^2-60x+36=0 are x\approx 0.64439…,x\approx 3.09987…