If c is a negative number in the equation x^n = c, how does that affect your ability to solve the equation for different values of n? Explain.

Question

If c is a negative number in the equation xn = c, how does that affect your ability to solve the equation for different values of n? Explain.

Answer 1

Hi Katiee,

 

If c is a negative number than there will be answers that are real numbers only if n is odd.

 

Lets look at a couple examples

 

if

 

x² = -4

 

then there are no solutions that are real numbers  (what number squared equals -4?)

 

on the other hand if we have

 

x³ = -8

 

then we do have solutions with real numbers

 

-2³ = -8  and therefore x = -2 is a real solution.

 

Hope this helps