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

The solutions to the equation 2+x^3-5x^2=0 are x\approx-0.59773…,x\approx 0.68044…,x\approx 4.91728…

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

The zeros of 2+x^3-5x^2=0 are x\approx-0.59773…,x\approx 0.68044…,x\approx 4.91728…

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

x \approx - 0.59773 \dots, x \approx 0.68044 \dots, x \approx 4.91728 \dots

Solution steps

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

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

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

Find one solution for

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

using Newton-Raphson:

x \approx - 0.59773 \dots

Apply long division:

\frac{x ^{3} - 5 x ^{2} + 2}{x + 0.59773 \dots} = x^{2} - 5.59773 \dots x + 3.34596 \dots

x^{2} - 5.59773 \dots x + 3.34596 \dots \approx 0

Find one solution for

x^{2} - 5.59773 \dots x + 3.34596 \dots = 0

using Newton-Raphson:

x \approx 0.68044 \dots

Apply long division:

\frac{x ^{2} - 5.59773 \dots x + 3.34596 \dots}{x - 0.68044 \dots} = x - 4.91728 \dots

x - 4.91728 \dots \approx 0

x \approx 4.91728 \dots

The solutions are

x \approx - 0.59773 \dots, x \approx 0.68044 \dots, x \approx 4.91728 \dots

(w - 3)^{2} (w + 1)^{2} = 0

5 = \frac{4}{3} π x^{3}

x^{8} + x^{5} + x^{2} - x + 1 = 0

8 x (x^{2} - 1)^{3} = 0

0 = y^{2} - y^{3}

What are the solutions to the equation 2+x^3-5x^2=0 ?
The solutions to the equation 2+x^3-5x^2=0 are x\approx-0.59773…,x\approx 0.68044…,x\approx 4.91728…
Find the zeros of 2+x^3-5x^2=0
The zeros of 2+x^3-5x^2=0 are x\approx-0.59773…,x\approx 0.68044…,x\approx 4.91728…