What are the solutions to the equation x^3+9x^2+27x+19=0 ?

The solutions to the equation x^3+9x^2+27x+19=0 are x=-1,x=-4+sqrt(3)i,x=-4-sqrt(3)i

Find the zeros of x^3+9x^2+27x+19=0

The zeros of x^3+9x^2+27x+19=0 are x=-1,x=-4+sqrt(3)i,x=-4-sqrt(3)i

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x^{3} + 9 x^{2} + 27 x + 19 = 0

x = - 1, x = - 4 + 3 i, x = - 4 - 3 i

Solution steps

x^{3} + 9 x^{2} + 27 x + 19 = 0

Factor

x^{3} + 9 x^{2} + 27 x + 19 : (x + 1) (x^{2} + 8 x + 19)

(x + 1) (x^{2} + 8 x + 19) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x^{2} + 8 x + 19 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x^{2} + 8 x + 19 = 0 : x = - 4 + 3 i, x = - 4 - 3 i

The solutions are

x = - 1, x = - 4 + 3 i, x = - 4 - 3 i

x^{3} = 3 x^{2}

2 x^{3} - 24 x^{2} + 64 x = 0

x^{3} + 4 x^{2} + 8 x + 10 = 0

x^{4} - 20 x^{2} + 99 = 0

3 x (8 x - 9) (x^{2} + 64) = 0

What are the solutions to the equation x^3+9x^2+27x+19=0 ?
The solutions to the equation x^3+9x^2+27x+19=0 are x=-1,x=-4+sqrt(3)i,x=-4-sqrt(3)i
Find the zeros of x^3+9x^2+27x+19=0
The zeros of x^3+9x^2+27x+19=0 are x=-1,x=-4+sqrt(3)i,x=-4-sqrt(3)i