What are the solutions to the equation x^3-3x-18=0 ?

The solutions to the equation x^3-3x-18=0 are x=3,x=-3/2+i(sqrt(15))/2 ,x=-3/2-i(sqrt(15))/2

Find the zeros of x^3-3x-18=0

The zeros of x^3-3x-18=0 are x=3,x=-3/2+i(sqrt(15))/2 ,x=-3/2-i(sqrt(15))/2

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x^{3} - 3 x - 18 = 0

x = 3, x = - \frac{3}{2} + i \frac{15}{2}, x = - \frac{3}{2} - i \frac{15}{2}

Solution steps

x^{3} - 3 x - 18 = 0

Factor

x^{3} - 3 x - 18 : (x - 3) (x^{2} + 3 x + 6)

(x - 3) (x^{2} + 3 x + 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or x^{2} + 3 x + 6 = 0

Solve

x - 3 = 0 : x = 3

Solve

x^{2} + 3 x + 6 = 0 : x = - \frac{3}{2} + i \frac{15}{2}, x = - \frac{3}{2} - i \frac{15}{2}

The solutions are

x = 3, x = - \frac{3}{2} + i \frac{15}{2}, x = - \frac{3}{2} - i \frac{15}{2}

x^{3} + 5 x^{2} + 4 x + 5 = 0

y, x = y^{5} - 2

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

24 x^{4} - 2 x^{2} - 1 = 0

x^{3} + x^{2} - 16 x + 20 = 0

What are the solutions to the equation x^3-3x-18=0 ?
The solutions to the equation x^3-3x-18=0 are x=3,x=-3/2+i(sqrt(15))/2 ,x=-3/2-i(sqrt(15))/2
Find the zeros of x^3-3x-18=0
The zeros of x^3-3x-18=0 are x=3,x=-3/2+i(sqrt(15))/2 ,x=-3/2-i(sqrt(15))/2