What are the solutions to the equation 3x^4+4x^3-12x^2+10=0 ?

The solutions to the equation 3x^4+4x^3-12x^2+10=0 are x\approx-0.87008…,x\approx-2.65999…

Find the zeros of 3x^4+4x^3-12x^2+10=0

The zeros of 3x^4+4x^3-12x^2+10=0 are x\approx-0.87008…,x\approx-2.65999…

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3 x^{4} + 4 x^{3} - 12 x^{2} + 10 = 0

x \approx - 0.87008 \dots, x \approx - 2.65999 \dots

Solution steps

3 x^{4} + 4 x^{3} - 12 x^{2} + 10 = 0

Find one solution for

3 x^{4} + 4 x^{3} - 12 x^{2} + 10 = 0

using Newton-Raphson:

x \approx - 0.87008 \dots

Apply long division:

\frac{3 x ^{4} + 4 x ^{3} - 12 x ^{2} + 10}{x + 0.87008 \dots} = 3 x^{3} + 1.38974 \dots x^{2} - 13.20919 \dots x + 11.49312 \dots

3 x^{3} + 1.38974 \dots x^{2} - 13.20919 \dots x + 11.49312 \dots \approx 0

Find one solution for

3 x^{3} + 1.38974 \dots x^{2} - 13.20919 \dots x + 11.49312 \dots = 0

using Newton-Raphson:

x \approx - 2.65999 \dots

Apply long division:

\frac{3 x ^{3} + 1.38974 \dots x ^{2} - 13.20919 \dots x + 11.49312 \dots}{x + 2.65999 \dots} = 3 x^{2} - 6.59022 \dots x + 4.32074 \dots

3 x^{2} - 6.59022 \dots x + 4.32074 \dots \approx 0

Find one solution for

3 x^{2} - 6.59022 \dots x + 4.32074 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 0.87008 \dots, x \approx - 2.65999 \dots

(x) = x^{3} - 3 x^{2} - 9 x - 5

x, x^{2} + (y - c b r t (x^{2}))^{2} = 25

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

9 x^{4} - 19 x^{2} + 2 = 0

(x + 2)^{3} = 30

What are the solutions to the equation 3x^4+4x^3-12x^2+10=0 ?
The solutions to the equation 3x^4+4x^3-12x^2+10=0 are x\approx-0.87008…,x\approx-2.65999…
Find the zeros of 3x^4+4x^3-12x^2+10=0
The zeros of 3x^4+4x^3-12x^2+10=0 are x\approx-0.87008…,x\approx-2.65999…