What are the solutions to the equation x^3+4x^2+x+4=0 ?

The solutions to the equation x^3+4x^2+x+4=0 are x=-4,x=i,x=-i

Find the zeros of x^3+4x^2+x+4=0

The zeros of x^3+4x^2+x+4=0 are x=-4,x=i,x=-i

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

x = - 4, x = i, x = - i

Solution steps

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

Factor

x^{3} + 4 x^{2} + x + 4 : (x + 4) (x^{2} + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 4 = 0 : x = - 4

Solve

x^{2} + 1 = 0 : x = i, x = - i

The solutions are

x = - 4, x = i, x = - i

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

0 = x^{3} - 13

z^{6} + 1 = 3 i

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

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

What are the solutions to the equation x^3+4x^2+x+4=0 ?
The solutions to the equation x^3+4x^2+x+4=0 are x=-4,x=i,x=-i
Find the zeros of x^3+4x^2+x+4=0
The zeros of x^3+4x^2+x+4=0 are x=-4,x=i,x=-i