What are the solutions to the equation roots 5x^3-3x^2+180x-108 ?

The solutions to the equation roots 5x^3-3x^2+180x-108 are x= 3/5 ,x=6i,x=-6i

Find the zeros of roots 5x^3-3x^2+180x-108

The zeros of roots 5x^3-3x^2+180x-108 are x= 3/5 ,x=6i,x=-6i

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roots

5 x^{3} - 3 x^{2} + 180 x - 108

x = \frac{3}{5}, x = 6 i, x = - 6 i

Solution steps

5 x^{3} - 3 x^{2} + 180 x - 108

The roots are the intercepts with the x-axis

(y = 0)

5 x^{3} - 3 x^{2} + 180 x - 108 = 0

Factor

5 x^{3} - 3 x^{2} + 180 x - 108 : (5 x - 3) (x^{2} + 36)

(5 x - 3) (x^{2} + 36) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

5 x - 3 = 0 or x^{2} + 36 = 0

Solve

5 x - 3 = 0 : x = \frac{3}{5}

Solve

x^{2} + 36 = 0 : x = 6 i, x = - 6 i

The solutions are

x = \frac{3}{5}, x = 6 i, x = - 6 i

y, x^{3} = 4 y^{2} + 4 y - 3

x^{4} - 128 \cdot x^{2} - 8192 \cdot x - 61440 = 0

6 x^{3} - 5 x - 1 = 0

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

x^{4} - 5 x^{3} + 6 x^{2} + 4 x - 8 = 0

What are the solutions to the equation roots 5x^3-3x^2+180x-108 ?
The solutions to the equation roots 5x^3-3x^2+180x-108 are x= 3/5 ,x=6i,x=-6i
Find the zeros of roots 5x^3-3x^2+180x-108
The zeros of roots 5x^3-3x^2+180x-108 are x= 3/5 ,x=6i,x=-6i