What are the solutions to the equation x^4+14x^3+14x^2+14x+13=0 ?

The solutions to the equation x^4+14x^3+14x^2+14x+13=0 are x=-1,x=-13,x=i,x=-i

Find the zeros of x^4+14x^3+14x^2+14x+13=0

The zeros of x^4+14x^3+14x^2+14x+13=0 are x=-1,x=-13,x=i,x=-i

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x^{4} + 14 x^{3} + 14 x^{2} + 14 x + 13 = 0

x = - 1, x = - 13, x = i, x = - i

Solution steps

x^{4} + 14 x^{3} + 14 x^{2} + 14 x + 13 = 0

Factor

x^{4} + 14 x^{3} + 14 x^{2} + 14 x + 13 : (x + 1) (x + 13) (x^{2} + 1)

(x + 1) (x + 13) (x^{2} + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x + 13 = 0 or x^{2} + 1 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x + 13 = 0 : x = - 13

Solve

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

The solutions are

x = - 1, x = - 13, x = i, x = - i

x^{3} = x + 3

x^{3} - 3 x^{2} - 8 x - 10 = 0

x^{4} + 19 x^{2} - 20 = 0

x, x^{3} - y^{2} = cy

10 x^{3} + x - 1 = 0

What are the solutions to the equation x^4+14x^3+14x^2+14x+13=0 ?
The solutions to the equation x^4+14x^3+14x^2+14x+13=0 are x=-1,x=-13,x=i,x=-i
Find the zeros of x^4+14x^3+14x^2+14x+13=0
The zeros of x^4+14x^3+14x^2+14x+13=0 are x=-1,x=-13,x=i,x=-i