What are the solutions to the equation 4x^5-x^3+32x^2-8=0 ?

The solutions to the equation 4x^5-x^3+32x^2-8=0 are x=-2,x=-1/2 ,x= 1/2 ,x=1+sqrt(3)i,x=1-sqrt(3)i

Find the zeros of 4x^5-x^3+32x^2-8=0

The zeros of 4x^5-x^3+32x^2-8=0 are x=-2,x=-1/2 ,x= 1/2 ,x=1+sqrt(3)i,x=1-sqrt(3)i

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4 x^{5} - x^{3} + 32 x^{2} - 8 = 0

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

Solution steps

4 x^{5} - x^{3} + 32 x^{2} - 8 = 0

Factor

4 x^{5} - x^{3} + 32 x^{2} - 8 : (x + 2) (2 x + 1) (2 x - 1) (x^{2} - 2 x + 4)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 2 = 0 or 2 x + 1 = 0 or 2 x - 1 = 0 or x^{2} - 2 x + 4 = 0

Solve

x + 2 = 0 : x = - 2

Solve

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

Solve

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

Solve

x^{2} - 2 x + 4 = 0 : x = 1 + 3 i, x = 1 - 3 i

The solutions are

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

- 2 x^{5} + 32 x^{3} = 0

(x + 1)^{3} = 8

(z^{2} + 5)^{3} = 0

- 3 x^{3} - 7 x^{2} - 12 x - 28 = 0

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

What are the solutions to the equation 4x^5-x^3+32x^2-8=0 ?
The solutions to the equation 4x^5-x^3+32x^2-8=0 are x=-2,x=-1/2 ,x= 1/2 ,x=1+sqrt(3)i,x=1-sqrt(3)i
Find the zeros of 4x^5-x^3+32x^2-8=0
The zeros of 4x^5-x^3+32x^2-8=0 are x=-2,x=-1/2 ,x= 1/2 ,x=1+sqrt(3)i,x=1-sqrt(3)i