What are the solutions to the equation x^7+5x^3+6=0 ?

The solutions to the equation x^7+5x^3+6=0 are x=-1

Find the zeros of x^7+5x^3+6=0

The zeros of x^7+5x^3+6=0 are x=-1

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x^{7} + 5 x^{3} + 6 = 0

x = - 1

Solution steps

x^{7} + 5 x^{3} + 6 = 0

Factor

x^{7} + 5 x^{3} + 6 : (x + 1) (x^{6} - x^{5} + x^{4} - x^{3} + 6 x^{2} - 6 x + 6)

(x + 1) (x^{6} - x^{5} + x^{4} - x^{3} + 6 x^{2} - 6 x + 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x^{6} - x^{5} + x^{4} - x^{3} + 6 x^{2} - 6 x + 6 = 0

Solve

x + 1 = 0 : x = - 1

Solve

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

No Solution for

x \in R

The solution is

x = - 1

2 x^{3} + 3 x^{2} - 8 x - 12 = 0

x^{3} = 125 x^{6}

x^{4} + 16 x - 12 = 0

2 x^{4} + 5 x^{3} - 12 x^{2} = 0

x^{3} - 6 x^{2} - 36 x = - 216

What are the solutions to the equation x^7+5x^3+6=0 ?
The solutions to the equation x^7+5x^3+6=0 are x=-1
Find the zeros of x^7+5x^3+6=0
The zeros of x^7+5x^3+6=0 are x=-1