What are the solutions to the equation 4x^3-6x^2+4x-1=0 ?

The solutions to the equation 4x^3-6x^2+4x-1=0 are x= 1/2 ,x= 1/2+i 1/2 ,x= 1/2-i 1/2

Find the zeros of 4x^3-6x^2+4x-1=0

The zeros of 4x^3-6x^2+4x-1=0 are x= 1/2 ,x= 1/2+i 1/2 ,x= 1/2-i 1/2

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4 x^{3} - 6 x^{2} + 4 x - 1 = 0

x = \frac{1}{2}, x = \frac{1}{2} + i \frac{1}{2}, x = \frac{1}{2} - i \frac{1}{2}

Solution steps

4 x^{3} - 6 x^{2} + 4 x - 1 = 0

Factor

4 x^{3} - 6 x^{2} + 4 x - 1 : (2 x - 1) (2 x^{2} - 2 x + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

2 x - 1 = 0 : x = \frac{1}{2}

Solve

2 x^{2} - 2 x + 1 = 0 : x = \frac{1}{2} + i \frac{1}{2}, x = \frac{1}{2} - i \frac{1}{2}

The solutions are

x = \frac{1}{2}, x = \frac{1}{2} + i \frac{1}{2}, x = \frac{1}{2} - i \frac{1}{2}

x^{4} - x^{2} - 20 = 0

t^{4} - 13 t^{2} + 36 = 0

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

x^{3} + 20 x = 9 x^{2}

x, x^{3} + y^{3} = 3

What are the solutions to the equation 4x^3-6x^2+4x-1=0 ?
The solutions to the equation 4x^3-6x^2+4x-1=0 are x= 1/2 ,x= 1/2+i 1/2 ,x= 1/2-i 1/2
Find the zeros of 4x^3-6x^2+4x-1=0
The zeros of 4x^3-6x^2+4x-1=0 are x= 1/2 ,x= 1/2+i 1/2 ,x= 1/2-i 1/2