What are the solutions to the equation x^3+5x^2+x+5=0 ?

The solutions to the equation x^3+5x^2+x+5=0 are x=-5,x=i,x=-i

Find the zeros of x^3+5x^2+x+5=0

The zeros of x^3+5x^2+x+5=0 are x=-5,x=i,x=-i

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

x = - 5, x = i, x = - i

Solution steps

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

Factor

x^{3} + 5 x^{2} + x + 5 : (x + 5) (x^{2} + 1)

(x + 5) (x^{2} + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 5 = 0 or x^{2} + 1 = 0

Solve

x + 5 = 0 : x = - 5

Solve

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

The solutions are

x = - 5, x = i, x = - i

2 x^{4} - 5 x^{2} - 12 = 0

8 = x^{3}

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

x^{5} - 4 x^{3} = 0

x^{3} - x + 3 = 0

What are the solutions to the equation x^3+5x^2+x+5=0 ?
The solutions to the equation x^3+5x^2+x+5=0 are x=-5,x=i,x=-i
Find the zeros of x^3+5x^2+x+5=0
The zeros of x^3+5x^2+x+5=0 are x=-5,x=i,x=-i