What are the solutions to the equation x=3x^4-x^2 ?

The solutions to the equation x=3x^4-x^2 are x=0,x\approx 0.85138…

Find the zeros of x=3x^4-x^2

The zeros of x=3x^4-x^2 are x=0,x\approx 0.85138…

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x = 3 x^{4} - x^{2}

x = 0, x \approx 0.85138 \dots

Solution steps

x = 3 x^{4} - x^{2}

Switch sides

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

Move

x

to the left side

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

3 x^{3} - x - 1 = 0 : x \approx 0.85138 \dots

The solutions are

x = 0, x \approx 0.85138 \dots

3 x^{3} - 2 x^{2} + 12 x - 8 = 0

x^{4} - 4 x^{3} + 2 x^{2} - 5 x + 7 = 0

4 x^{4} - 4 x^{2} - 1 = 0

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

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

What are the solutions to the equation x=3x^4-x^2 ?
The solutions to the equation x=3x^4-x^2 are x=0,x\approx 0.85138…
Find the zeros of x=3x^4-x^2
The zeros of x=3x^4-x^2 are x=0,x\approx 0.85138…