What are the solutions to the equation x^3-5x^2-30x-54=0 ?

The solutions to the equation x^3-5x^2-30x-54=0 are x=9,x=-2+sqrt(2)i,x=-2-sqrt(2)i

Find the zeros of x^3-5x^2-30x-54=0

The zeros of x^3-5x^2-30x-54=0 are x=9,x=-2+sqrt(2)i,x=-2-sqrt(2)i

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x^{3} - 5 x^{2} - 30 x - 54 = 0

x = 9, x = - 2 + 2 i, x = - 2 - 2 i

Solution steps

x^{3} - 5 x^{2} - 30 x - 54 = 0

Factor

x^{3} - 5 x^{2} - 30 x - 54 : (x - 9) (x^{2} + 4 x + 6)

(x - 9) (x^{2} + 4 x + 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 9 = 0 or x^{2} + 4 x + 6 = 0

Solve

x - 9 = 0 : x = 9

Solve

x^{2} + 4 x + 6 = 0 : x = - 2 + 2 i, x = - 2 - 2 i

The solutions are

x = 9, x = - 2 + 2 i, x = - 2 - 2 i

4 x^{3} + 3 x^{2} + 100 x + 75 = 0

4 x^{3} = x

x, 2 y^{2} = x^{3}

x^{3} + 4 x^{2} - 11 x - 30 = 0

z^{4} = 3

What are the solutions to the equation x^3-5x^2-30x-54=0 ?
The solutions to the equation x^3-5x^2-30x-54=0 are x=9,x=-2+sqrt(2)i,x=-2-sqrt(2)i
Find the zeros of x^3-5x^2-30x-54=0
The zeros of x^3-5x^2-30x-54=0 are x=9,x=-2+sqrt(2)i,x=-2-sqrt(2)i