What are the solutions to the equation 2x^4-3x^3-12x^2-6x+5=0 ?

The solutions to the equation 2x^4-3x^3-12x^2-6x+5=0 are x\approx 0.43178…,x\approx 3.43768…

Find the zeros of 2x^4-3x^3-12x^2-6x+5=0

The zeros of 2x^4-3x^3-12x^2-6x+5=0 are x\approx 0.43178…,x\approx 3.43768…

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2 x^{4} - 3 x^{3} - 12 x^{2} - 6 x + 5 = 0

x \approx 0.43178 \dots, x \approx 3.43768 \dots

Solution steps

2 x^{4} - 3 x^{3} - 12 x^{2} - 6 x + 5 = 0

Find one solution for

2 x^{4} - 3 x^{3} - 12 x^{2} - 6 x + 5 = 0

using Newton-Raphson:

x \approx 0.43178 \dots

Apply long division:

\frac{2 x ^{4} - 3 x ^{3} - 12 x ^{2} - 6 x + 5}{x - 0.43178 \dots} = 2 x^{3} - 2.13642 \dots x^{2} - 12.92248 \dots x - 11.57976 \dots

2 x^{3} - 2.13642 \dots x^{2} - 12.92248 \dots x - 11.57976 \dots \approx 0

Find one solution for

2 x^{3} - 2.13642 \dots x^{2} - 12.92248 \dots x - 11.57976 \dots = 0

using Newton-Raphson:

x \approx 3.43768 \dots

Apply long division:

\frac{2 x ^{3} - 2.13642 \dots x ^{2} - 12.92248 \dots x - 11.57976 \dots}{x - 3.43768 \dots} = 2 x^{2} + 4.73893 \dots x + 3.36848 \dots

2 x^{2} + 4.73893 \dots x + 3.36848 \dots \approx 0

Find one solution for

2 x^{2} + 4.73893 \dots x + 3.36848 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.43178 \dots, x \approx 3.43768 \dots

3 x^{3} + 19 x^{2} + 21 x + 5 = 0

3 x^{3} + 4 x^{2} - 45 x - 60 = 0

x^{4} + 34 x^{2} + 225 = 0

x^{10} = 1.4567

t^{3} = 4

What are the solutions to the equation 2x^4-3x^3-12x^2-6x+5=0 ?
The solutions to the equation 2x^4-3x^3-12x^2-6x+5=0 are x\approx 0.43178…,x\approx 3.43768…
Find the zeros of 2x^4-3x^3-12x^2-6x+5=0
The zeros of 2x^4-3x^3-12x^2-6x+5=0 are x\approx 0.43178…,x\approx 3.43768…