What are the solutions to the equation x^4+12x^3+12x^2+12x+11=0 ?

The solutions to the equation x^4+12x^3+12x^2+12x+11=0 are x=-1,x=-11,x=i,x=-i

Find the zeros of x^4+12x^3+12x^2+12x+11=0

The zeros of x^4+12x^3+12x^2+12x+11=0 are x=-1,x=-11,x=i,x=-i

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x^{4} + 12 x^{3} + 12 x^{2} + 12 x + 11 = 0

x = - 1, x = - 11, x = i, x = - i

Solution steps

x^{4} + 12 x^{3} + 12 x^{2} + 12 x + 11 = 0

Factor

x^{4} + 12 x^{3} + 12 x^{2} + 12 x + 11 : (x + 1) (x + 11) (x^{2} + 1)

(x + 1) (x + 11) (x^{2} + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x + 11 = 0 or x^{2} + 1 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x + 11 = 0 : x = - 11

Solve

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

The solutions are

x = - 1, x = - 11, x = i, x = - i

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

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

\frac{1}{3} x^{3} = 0

x (2 x^{2} - 1) = 0

2 x^{3} - 11 x^{2} + 12 x + 9 = 0

What are the solutions to the equation x^4+12x^3+12x^2+12x+11=0 ?
The solutions to the equation x^4+12x^3+12x^2+12x+11=0 are x=-1,x=-11,x=i,x=-i
Find the zeros of x^4+12x^3+12x^2+12x+11=0
The zeros of x^4+12x^3+12x^2+12x+11=0 are x=-1,x=-11,x=i,x=-i