What are the solutions to the equation 4x-2x^4-2=0 ?

The solutions to the equation 4x-2x^4-2=0 are x=1,x\approx 0.54368…

Find the zeros of 4x-2x^4-2=0

The zeros of 4x-2x^4-2=0 are x=1,x\approx 0.54368…

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4 x - 2 x^{4} - 2 = 0

x = 1, x \approx 0.54368 \dots

Solution steps

4 x - 2 x^{4} - 2 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

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

Factor

- 2 x^{4} + 4 x - 2 : - 2 (x - 1) (x^{3} + x^{2} + x - 1)

- 2 (x - 1) (x^{3} + x^{2} + x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

x^{3} + x^{2} + x - 1 = 0 : x \approx 0.54368 \dots

The solutions are

x = 1, x \approx 0.54368 \dots

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

x, (2 x^{4} \cdot y^{4} - 4 x^{2} \cdot y) = (2 x^{2} \cdot y)

(1 + r)^{6} = 8000

x^{4} (x - 1) + x^{3} (x - 1) = 0

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

What are the solutions to the equation 4x-2x^4-2=0 ?
The solutions to the equation 4x-2x^4-2=0 are x=1,x\approx 0.54368…
Find the zeros of 4x-2x^4-2=0
The zeros of 4x-2x^4-2=0 are x=1,x\approx 0.54368…