What are the solutions to the equation x^5+2x^3+10x^2+x+10=0 ?

The solutions to the equation x^5+2x^3+10x^2+x+10=0 are x=-2

Find the zeros of x^5+2x^3+10x^2+x+10=0

The zeros of x^5+2x^3+10x^2+x+10=0 are x=-2

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x^{5} + 2 x^{3} + 10 x^{2} + x + 10 = 0

x = - 2

Solution steps

x^{5} + 2 x^{3} + 10 x^{2} + x + 10 = 0

Factor

x^{5} + 2 x^{3} + 10 x^{2} + x + 10 : (x + 2) (x^{4} - 2 x^{3} + 6 x^{2} - 2 x + 5)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 2 = 0 : x = - 2

Solve

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

No Solution for

x \in R

The solution is

x = - 2

y, x + x^{3} = y + y^{3}

y, x^{2} + 3 x^{4} y = 4

2 x^{5} + 3 x^{4} - 2 x - 3

15 x^{4} - 12 x^{2} - 3 = 0

x^{4} + 25 = 26 x^{2}

What are the solutions to the equation x^5+2x^3+10x^2+x+10=0 ?
The solutions to the equation x^5+2x^3+10x^2+x+10=0 are x=-2
Find the zeros of x^5+2x^3+10x^2+x+10=0
The zeros of x^5+2x^3+10x^2+x+10=0 are x=-2