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

The solutions to the equation 4x^3-6x^2+4x=0 are x=0,x= 3/4+i(sqrt(7))/4 ,x= 3/4-i(sqrt(7))/4

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

The zeros of 4x^3-6x^2+4x=0 are x=0,x= 3/4+i(sqrt(7))/4 ,x= 3/4-i(sqrt(7))/4

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

x = 0, x = \frac{3}{4} + i \frac{7}{4}, x = \frac{3}{4} - i \frac{7}{4}

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

2 x^{2} - 3 x + 2 = 0 : x = \frac{3}{4} + i \frac{7}{4}, x = \frac{3}{4} - i \frac{7}{4}

The solutions are

x = 0, x = \frac{3}{4} + i \frac{7}{4}, x = \frac{3}{4} - i \frac{7}{4}

x^{4} + 2 x^{3} + x^{2} + 8 x - 12

y, x^{5} + y^{5} = 16

x^{4} + 4 x^{3} + 9 x^{2} + 10 x + 7 = 0

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

x^{3} - x^{2} - 8 x + 6 = 0

What are the solutions to the equation 4x^3-6x^2+4x=0 ?
The solutions to the equation 4x^3-6x^2+4x=0 are x=0,x= 3/4+i(sqrt(7))/4 ,x= 3/4-i(sqrt(7))/4
Find the zeros of 4x^3-6x^2+4x=0
The zeros of 4x^3-6x^2+4x=0 are x=0,x= 3/4+i(sqrt(7))/4 ,x= 3/4-i(sqrt(7))/4