What are the solutions to the equation 2x^3-x^2+32x-16=0 ?

The solutions to the equation 2x^3-x^2+32x-16=0 are x= 1/2 ,x=4i,x=-4i

Find the zeros of 2x^3-x^2+32x-16=0

The zeros of 2x^3-x^2+32x-16=0 are x= 1/2 ,x=4i,x=-4i

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2 x^{3} - x^{2} + 32 x - 16 = 0

x = \frac{1}{2}, x = 4 i, x = - 4 i

Solution steps

2 x^{3} - x^{2} + 32 x - 16 = 0

Factor

2 x^{3} - x^{2} + 32 x - 16 : (2 x - 1) (x^{2} + 16)

(2 x - 1) (x^{2} + 16) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 x - 1 = 0 or x^{2} + 16 = 0

Solve

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

Solve

x^{2} + 16 = 0 : x = 4 i, x = - 4 i

The solutions are

x = \frac{1}{2}, x = 4 i, x = - 4 i

x^{4} - 10 x + 5 = 0

2 x^{3} - 2 x^{2} - 5 x = 3

x^{4} + 12 x^{3} - 64 x^{2} = 0

x^{4} + 3 x^{2} - 54 = 0

x^{5} + x^{2} + 1 = 0

What are the solutions to the equation 2x^3-x^2+32x-16=0 ?
The solutions to the equation 2x^3-x^2+32x-16=0 are x= 1/2 ,x=4i,x=-4i
Find the zeros of 2x^3-x^2+32x-16=0
The zeros of 2x^3-x^2+32x-16=0 are x= 1/2 ,x=4i,x=-4i