What are the solutions to the equation 3x^4+22x^3+61x^2+76x+26=0 ?

The solutions to the equation 3x^4+22x^3+61x^2+76x+26=0 are x\approx-0.52350…,x\approx-3.16344…

Find the zeros of 3x^4+22x^3+61x^2+76x+26=0

The zeros of 3x^4+22x^3+61x^2+76x+26=0 are x\approx-0.52350…,x\approx-3.16344…

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3 x^{4} + 22 x^{3} + 61 x^{2} + 76 x + 26 = 0

x \approx - 0.52350 \dots, x \approx - 3.16344 \dots

Solution steps

3 x^{4} + 22 x^{3} + 61 x^{2} + 76 x + 26 = 0

Find one solution for

3 x^{4} + 22 x^{3} + 61 x^{2} + 76 x + 26 = 0

using Newton-Raphson:

x \approx - 0.52350 \dots

Apply long division:

\frac{3 x ^{4} + 22 x ^{3} + 61 x ^{2} + 76 x + 26}{x + 0.52350 \dots} = 3 x^{3} + 20.42947 \dots x^{2} + 50.30499 \dots x + 49.66490 \dots

3 x^{3} + 20.42947 \dots x^{2} + 50.30499 \dots x + 49.66490 \dots \approx 0

Find one solution for

3 x^{3} + 20.42947 \dots x^{2} + 50.30499 \dots x + 49.66490 \dots = 0

using Newton-Raphson:

x \approx - 3.16344 \dots

Apply long division:

\frac{3 x ^{3} + 20.42947 \dots x ^{2} + 50.30499 \dots x + 49.66490 \dots}{x + 3.16344 \dots} = 3 x^{2} + 10.93914 \dots x + 15.69963 \dots

3 x^{2} + 10.93914 \dots x + 15.69963 \dots \approx 0

Find one solution for

3 x^{2} + 10.93914 \dots x + 15.69963 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 0.52350 \dots, x \approx - 3.16344 \dots

r^{3} + 4 r = 0

x^{4} + 3 x^{3} + 3 x^{2} + x = 0

y^{4} - 1 = 0

x^{5} - 2.2 x^{4} - 6.61 x^{3} + 8.602 x^{2} = 0

p^{4} - 81 = 0

What are the solutions to the equation 3x^4+22x^3+61x^2+76x+26=0 ?
The solutions to the equation 3x^4+22x^3+61x^2+76x+26=0 are x\approx-0.52350…,x\approx-3.16344…
Find the zeros of 3x^4+22x^3+61x^2+76x+26=0
The zeros of 3x^4+22x^3+61x^2+76x+26=0 are x\approx-0.52350…,x\approx-3.16344…