What are the solutions to the equation 2x^4-4x^3-4^2+6x+9=0 ?

The solutions to the equation 2x^4-4x^3-4^2+6x+9=0 are x\approx 1.67546…,x\approx-1.30931…

Find the zeros of 2x^4-4x^3-4^2+6x+9=0

The zeros of 2x^4-4x^3-4^2+6x+9=0 are x\approx 1.67546…,x\approx-1.30931…

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2 x^{4} - 4 x^{3} - 4^{2} + 6 x + 9 = 0

x \approx 1.67546 \dots, x \approx - 1.30931 \dots

Solution steps

2 x^{4} - 4 x^{3} - 4^{2} + 6 x + 9 = 0

Expand

2 x^{4} - 4 x^{3} - 4^{2} + 6 x + 9 : 2 x^{4} - 4 x^{3} + 6 x - 7

2 x^{4} - 4 x^{3} + 6 x - 7 = 0

Find one solution for

2 x^{4} - 4 x^{3} + 6 x - 7 = 0

using Newton-Raphson:

x \approx 1.67546 \dots

Apply long division:

\frac{2 x ^{4} - 4 x ^{3} + 6 x - 7}{x - 1.67546 \dots} = 2 x^{3} - 0.64906 \dots x^{2} - 1.08749 \dots x + 4.17794 \dots

2 x^{3} - 0.64906 \dots x^{2} - 1.08749 \dots x + 4.17794 \dots \approx 0

Find one solution for

2 x^{3} - 0.64906 \dots x^{2} - 1.08749 \dots x + 4.17794 \dots = 0

using Newton-Raphson:

x \approx - 1.30931 \dots

Apply long division:

\frac{2 x ^{3} - 0.64906 \dots x ^{2} - 1.08749 \dots x + 4.17794 \dots}{x + 1.30931 \dots} = 2 x^{2} - 3.26769 \dots x + 3.19094 \dots

2 x^{2} - 3.26769 \dots x + 3.19094 \dots \approx 0

Find one solution for

2 x^{2} - 3.26769 \dots x + 3.19094 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.67546 \dots, x \approx - 1.30931 \dots

x^{3} + 20 x^{2} + 64 x - 100 = 0

- 3 x (36 x^{2} - 25) (x^{2} - 2) = 0

x^{3} - 14 x^{2} = + 56 - 64

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

x^{5} + 30 = 0

What are the solutions to the equation 2x^4-4x^3-4^2+6x+9=0 ?
The solutions to the equation 2x^4-4x^3-4^2+6x+9=0 are x\approx 1.67546…,x\approx-1.30931…
Find the zeros of 2x^4-4x^3-4^2+6x+9=0
The zeros of 2x^4-4x^3-4^2+6x+9=0 are x\approx 1.67546…,x\approx-1.30931…