What are the solutions to the equation x^4+6x^2+6x^3+6x+5=0 ?

The solutions to the equation x^4+6x^2+6x^3+6x+5=0 are x=-1,x=-5,x=i,x=-i

Find the zeros of x^4+6x^2+6x^3+6x+5=0

The zeros of x^4+6x^2+6x^3+6x+5=0 are x=-1,x=-5,x=i,x=-i

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

x = - 1, x = - 5, x = i, x = - i

Solution steps

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

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

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

Factor

x^{4} + 6 x^{3} + 6 x^{2} + 6 x + 5 : (x + 1) (x + 5) (x^{2} + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 1 = 0 : x = - 1

Solve

x + 5 = 0 : x = - 5

Solve

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

The solutions are

x = - 1, x = - 5, x = i, x = - i

m^{3} - 6 m^{2} + 12 m - 8 = 0

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

25 x^{4} + 9 = 34 x^{2}

25 x^{4} - 4 x^{2} = 0

2 x^{3} + 12 x^{2} + 18 x = 0

What are the solutions to the equation x^4+6x^2+6x^3+6x+5=0 ?
The solutions to the equation x^4+6x^2+6x^3+6x+5=0 are x=-1,x=-5,x=i,x=-i
Find the zeros of x^4+6x^2+6x^3+6x+5=0
The zeros of x^4+6x^2+6x^3+6x+5=0 are x=-1,x=-5,x=i,x=-i