What are the solutions to the equation 3x^4+5x^3+3x^2+x=20 ?

The solutions to the equation 3x^4+5x^3+3x^2+x=20 are x\approx 1.19241…,x\approx-2.04092…

Find the zeros of 3x^4+5x^3+3x^2+x=20

The zeros of 3x^4+5x^3+3x^2+x=20 are x\approx 1.19241…,x\approx-2.04092…

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3 x^{4} + 5 x^{3} + 3 x^{2} + x = 20

x \approx 1.19241 \dots, x \approx - 2.04092 \dots

Solution steps

3 x^{4} + 5 x^{3} + 3 x^{2} + x = 20

Move

20

to the left side

3 x^{4} + 5 x^{3} + 3 x^{2} + x - 20 = 0

Find one solution for

3 x^{4} + 5 x^{3} + 3 x^{2} + x - 20 = 0

using Newton-Raphson:

x \approx 1.19241 \dots

Apply long division:

\frac{3 x ^{4} + 5 x ^{3} + 3 x ^{2} + x - 20}{x - 1.19241 \dots} = 3 x^{3} + 8.57723 \dots x^{2} + 13.22759 \dots x + 16.77273 \dots

3 x^{3} + 8.57723 \dots x^{2} + 13.22759 \dots x + 16.77273 \dots \approx 0

Find one solution for

3 x^{3} + 8.57723 \dots x^{2} + 13.22759 \dots x + 16.77273 \dots = 0

using Newton-Raphson:

x \approx - 2.04092 \dots

Apply long division:

\frac{3 x ^{3} + 8.57723 \dots x ^{2} + 13.22759 \dots x + 16.77273 \dots}{x + 2.04092 \dots} = 3 x^{2} + 2.45446 \dots x + 8.21821 \dots

3 x^{2} + 2.45446 \dots x + 8.21821 \dots \approx 0

Find one solution for

3 x^{2} + 2.45446 \dots x + 8.21821 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.19241 \dots, x \approx - 2.04092 \dots

- 5.3 t^{3} + 21 t^{2} + 16 t = 0

4 x^{2} (x - 3) = 0

(4 m^{2} + 2)^{2} = 0

x^{5} + 1024 = 0

x^{3} + 2 x^{2} - 49 x - 98 = 0

What are the solutions to the equation 3x^4+5x^3+3x^2+x=20 ?
The solutions to the equation 3x^4+5x^3+3x^2+x=20 are x\approx 1.19241…,x\approx-2.04092…
Find the zeros of 3x^4+5x^3+3x^2+x=20
The zeros of 3x^4+5x^3+3x^2+x=20 are x\approx 1.19241…,x\approx-2.04092…