What are the solutions to the equation 8x^3-12x^2+6x-65=0 ?

The solutions to the equation 8x^3-12x^2+6x-65=0 are x= 5/2 ,x=-1/2+sqrt(3)i,x=-1/2-sqrt(3)i

Find the zeros of 8x^3-12x^2+6x-65=0

The zeros of 8x^3-12x^2+6x-65=0 are x= 5/2 ,x=-1/2+sqrt(3)i,x=-1/2-sqrt(3)i

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8 x^{3} - 12 x^{2} + 6 x - 65 = 0

x = \frac{5}{2}, x = - \frac{1}{2} + 3 i, x = - \frac{1}{2} - 3 i

Solution steps

8 x^{3} - 12 x^{2} + 6 x - 65 = 0

Factor

8 x^{3} - 12 x^{2} + 6 x - 65 : (2 x - 5) (4 x^{2} + 4 x + 13)

(2 x - 5) (4 x^{2} + 4 x + 13) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 x - 5 = 0 or 4 x^{2} + 4 x + 13 = 0

Solve

2 x - 5 = 0 : x = \frac{5}{2}

Solve

4 x^{2} + 4 x + 13 = 0 : x = - \frac{1}{2} + 3 i, x = - \frac{1}{2} - 3 i

The solutions are

x = \frac{5}{2}, x = - \frac{1}{2} + 3 i, x = - \frac{1}{2} - 3 i

2 x^{1} + x^{2} - x^{3} + x^{4} = - 2

x^{3} = 5 x^{2} - 6 x

(3 p + 7) (3 p - 7) (p + 8) = 0

x \cdot (2 x - 4)^{2} = 0

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

What are the solutions to the equation 8x^3-12x^2+6x-65=0 ?
The solutions to the equation 8x^3-12x^2+6x-65=0 are x= 5/2 ,x=-1/2+sqrt(3)i,x=-1/2-sqrt(3)i
Find the zeros of 8x^3-12x^2+6x-65=0
The zeros of 8x^3-12x^2+6x-65=0 are x= 5/2 ,x=-1/2+sqrt(3)i,x=-1/2-sqrt(3)i