What are the solutions to the equation 3x^4-24x^3+4x^2-29x-67=0 ?

The solutions to the equation 3x^4-24x^3+4x^2-29x-67=0 are x\approx-1.05541…,x\approx 8.02709…

Find the zeros of 3x^4-24x^3+4x^2-29x-67=0

The zeros of 3x^4-24x^3+4x^2-29x-67=0 are x\approx-1.05541…,x\approx 8.02709…

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3 x^{4} - 24 x^{3} + 4 x^{2} - 29 x - 67 = 0

x \approx - 1.05541 \dots, x \approx 8.02709 \dots

Solution steps

3 x^{4} - 24 x^{3} + 4 x^{2} - 29 x - 67 = 0

Find one solution for

3 x^{4} - 24 x^{3} + 4 x^{2} - 29 x - 67 = 0

using Newton-Raphson:

x \approx - 1.05541 \dots

Apply long division:

\frac{3 x ^{4} - 24 x ^{3} + 4 x ^{2} - 29 x - 67}{x + 1.05541 \dots} = 3 x^{3} - 27.16624 \dots x^{2} + 32.67165 \dots x - 63.48214 \dots

3 x^{3} - 27.16624 \dots x^{2} + 32.67165 \dots x - 63.48214 \dots \approx 0

Find one solution for

3 x^{3} - 27.16624 \dots x^{2} + 32.67165 \dots x - 63.48214 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

x \approx 8.02709 \dots

The solutions are

x \approx - 1.05541 \dots, x \approx 8.02709 \dots

x^{3} + 2 x + 1

x^{3} + 2 x + 2

x^{6} - 3 x^{4} - x^{3} + 2 x^{2} - x - 1 = 0

3 x^{3} - 4 x = 0

s^{3} + 3.5 s^{2} + 1.75 s + 1.5 = 0

What are the solutions to the equation 3x^4-24x^3+4x^2-29x-67=0 ?
The solutions to the equation 3x^4-24x^3+4x^2-29x-67=0 are x\approx-1.05541…,x\approx 8.02709…
Find the zeros of 3x^4-24x^3+4x^2-29x-67=0
The zeros of 3x^4-24x^3+4x^2-29x-67=0 are x\approx-1.05541…,x\approx 8.02709…