Question

how many real roots does the equation x^7 + x
have

Answer 1

Hmm...that is an expression. You need to add "=sumthing" to make it an equation.
Maybe it's x^7+x=0 ?

Answer 2

oh sorry i forgot to add that part

Answer 3

No prob. Let's work it together.
First we factor out x: x(x^6+1)=0
okay?

Answer 4

okay

Answer 5

So that means that either x = 0 (first real root) or x^6+1=0 ok?

Answer 6

i see, so we just solve it by factoring? no need to use the rule of signs or anything fancy?

Answer 7

We will do something a bit fancy with x^6+1=0
So that means that x^6=-1
Now, there is no real value for x that can be raised to power 6, to get a value of -1.
That means that there is only one real root for the original equation: x=0

Answer 8

okay, thanks for the help

Answer 9

You're welcome :)