What are the solutions to the equation (s^3-s^2+s-1)=s^2+3s+4 ?

The solutions to the equation (s^3-s^2+s-1)=s^2+3s+4 are s\approx 3.14266…

Find the zeros of (s^3-s^2+s-1)=s^2+3s+4

The zeros of (s^3-s^2+s-1)=s^2+3s+4 are s\approx 3.14266…

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(s^{3} - s^{2} + s - 1) = s^{2} + 3 s + 4

s \approx 3.14266 \dots

Solution steps

(s^{3} - s^{2} + s - 1) = s^{2} + 3 s + 4

Refine

s^{3} - s^{2} + s - 1 = s^{2} + 3 s + 4

Move

4

to the left side

s^{3} - s^{2} + s - 5 = s^{2} + 3 s

Move

3 s

to the left side

s^{3} - s^{2} - 2 s - 5 = s^{2}

Move

s^{2}

to the left side

s^{3} - 2 s^{2} - 2 s - 5 = 0

Find one solution for

s^{3} - 2 s^{2} - 2 s - 5 = 0

using Newton-Raphson:

s \approx 3.14266 \dots

Apply long division:

\frac{s ^{3} - 2 s ^{2} - 2 s - 5}{s - 3.14266 \dots} = s^{2} + 1.14266 \dots s + 1.59100 \dots

s^{2} + 1.14266 \dots s + 1.59100 \dots \approx 0

Find one solution for

s^{2} + 1.14266 \dots s + 1.59100 \dots = 0

using Newton-Raphson:

No Solution for

s \in R

The solution is

s \approx 3.14266 \dots

8 x^{4} = 6 x^{3}

x^{3} + 7 x^{2} + 2 x + 14 = 0

x^{4} - 16 x^{3} + 76 x^{2} - 96 x + 16 = 0

3 x^{3} + x = 0

2 (x + 6) (16 x^{2} - 25) = 0

What are the solutions to the equation (s^3-s^2+s-1)=s^2+3s+4 ?
The solutions to the equation (s^3-s^2+s-1)=s^2+3s+4 are s\approx 3.14266…
Find the zeros of (s^3-s^2+s-1)=s^2+3s+4
The zeros of (s^3-s^2+s-1)=s^2+3s+4 are s\approx 3.14266…