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

The solutions to the equation 4y^4-4y=0 are y=0,y=1,y=-1/2+(sqrt(3))/2 i,y=-1/2-(sqrt(3))/2 i

Find the zeros of 4y^4-4y=0

The zeros of 4y^4-4y=0 are y=0,y=1,y=-1/2+(sqrt(3))/2 i,y=-1/2-(sqrt(3))/2 i

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4 y^{4} - 4 y = 0

y = 0, y = 1, y = - \frac{1}{2} + \frac{3}{2} i, y = - \frac{1}{2} - \frac{3}{2} i

Solution steps

4 y^{4} - 4 y = 0

Factor

4 y^{4} - 4 y : 4 y (y^{3} - 1)

4 y (y^{3} - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

y^{3} - 1 = 0 : y = 1, y = - \frac{1}{2} + \frac{3}{2} i, y = - \frac{1}{2} - \frac{3}{2} i

The solutions are

y = 0, y = 1, y = - \frac{1}{2} + \frac{3}{2} i, y = - \frac{1}{2} - \frac{3}{2} i

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

4 π x^{2} = \frac{4 π x ^{3}}{3}

9 x^{5} - 72 x^{2} = 0

6 = 1 - 2 n^{5}

x^{4} = (3 x - 70)^{2}

What are the solutions to the equation 4y^4-4y=0 ?
The solutions to the equation 4y^4-4y=0 are y=0,y=1,y=-1/2+(sqrt(3))/2 i,y=-1/2-(sqrt(3))/2 i
Find the zeros of 4y^4-4y=0
The zeros of 4y^4-4y=0 are y=0,y=1,y=-1/2+(sqrt(3))/2 i,y=-1/2-(sqrt(3))/2 i