What are the solutions to the equation x^3-5x^2+3x= 1/2 ?

The solutions to the equation x^3-5x^2+3x= 1/2 are x\approx 4.33449…

Find the zeros of x^3-5x^2+3x= 1/2

The zeros of x^3-5x^2+3x= 1/2 are x\approx 4.33449…

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x^{3} - 5 x^{2} + 3 x = \frac{1}{2}

x \approx 4.33449 \dots

Solution steps

x^{3} - 5 x^{2} + 3 x = \frac{1}{2}

Multiply both sides by

2

2 x^{3} - 10 x^{2} + 6 x = 1

Move

1

to the left side

2 x^{3} - 10 x^{2} + 6 x - 1 = 0

Find one solution for

2 x^{3} - 10 x^{2} + 6 x - 1 = 0

using Newton-Raphson:

x \approx 4.33449 \dots

Apply long division:

\frac{2 x ^{3} - 10 x ^{2} + 6 x - 1}{x - 4.33449 \dots} = 2 x^{2} - 1.33101 \dots x + 0.23070 \dots

2 x^{2} - 1.33101 \dots x + 0.23070 \dots \approx 0

Find one solution for

2 x^{2} - 1.33101 \dots x + 0.23070 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 4.33449 \dots

2 x^{3} - 3 x^{2} - 2 x + 3 = x^{2} - 1

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

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

9 x^{4} + 69 x^{3} - 29 x^{2} - 41 x - 8 = 0

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

What are the solutions to the equation x^3-5x^2+3x= 1/2 ?
The solutions to the equation x^3-5x^2+3x= 1/2 are x\approx 4.33449…
Find the zeros of x^3-5x^2+3x= 1/2
The zeros of x^3-5x^2+3x= 1/2 are x\approx 4.33449…