What are the solutions to the equation 12x^5-8x^4-12x+8=0 ?

The solutions to the equation 12x^5-8x^4-12x+8=0 are x= 2/3 ,x=i,x=-i,x=-1,x=1

Find the zeros of 12x^5-8x^4-12x+8=0

The zeros of 12x^5-8x^4-12x+8=0 are x= 2/3 ,x=i,x=-i,x=-1,x=1

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12 x^{5} - 8 x^{4} - 12 x + 8 = 0

x = \frac{2}{3}, x = i, x = - i, x = - 1, x = 1

Solution steps

12 x^{5} - 8 x^{4} - 12 x + 8 = 0

Factor

12 x^{5} - 8 x^{4} - 12 x + 8 : 4 (3 x - 2) (x^{2} + 1) (x + 1) (x - 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

3 x - 2 = 0 : x = \frac{2}{3}

Solve

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

Solve

x + 1 = 0 : x = - 1

Solve

x - 1 = 0 : x = 1

The solutions are

x = \frac{2}{3}, x = i, x = - i, x = - 1, x = 1

2 x^{3} + x = 4

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

x^{3} + 6 x^{2} - 13 x - 78 = 0

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

x^{4} + 10 x^{2} - 9 = 0

What are the solutions to the equation 12x^5-8x^4-12x+8=0 ?
The solutions to the equation 12x^5-8x^4-12x+8=0 are x= 2/3 ,x=i,x=-i,x=-1,x=1
Find the zeros of 12x^5-8x^4-12x+8=0
The zeros of 12x^5-8x^4-12x+8=0 are x= 2/3 ,x=i,x=-i,x=-1,x=1