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

The solutions to the equation x^4-x^2+x=0 are x=0,x\approx-1.32471…

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

The zeros of x^4-x^2+x=0 are x=0,x\approx-1.32471…

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

x = 0, x \approx - 1.32471 \dots

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x^{3} - x + 1 = 0 : x \approx - 1.32471 \dots

The solutions are

x = 0, x \approx - 1.32471 \dots

2 = (1 + x)^{7}

x^{3} + 6 = 0

x^{4} - 4 x^{3} - 2 x^{2} + 12 x + 9 = 0

(2 x)^{3} = 128

x^{3} = 0.125

What are the solutions to the equation x^4-x^2+x=0 ?
The solutions to the equation x^4-x^2+x=0 are x=0,x\approx-1.32471…
Find the zeros of x^4-x^2+x=0
The zeros of x^4-x^2+x=0 are x=0,x\approx-1.32471…