How do I figure out how many roots there are in a function?

(Explain steps and post formulas)

 

Example1: y= (x+3)^2 -2

 

 

Example2: y = (7x - 1)(x^2 - 2)

 

 

 

Thanx

try this

http://jwilson.coe.uga.edu/emt669/Student.Folders/Frietag.Mark/Homepage/roots/roots.html

When [math]ax^2+bx+c=0[/math].

You should know that [math]x=\frac{-b+(b^2-4ac)^\frac{1}{2}}{2a}[/math]

If you look at the [math]b^2-4ac[/math] you'll see that it must be [math]>0[/math] or you wont have a real number so you can see if a function has any roots at all simply by looking at that bit.

You can tell how many (complex) roots a polynomial has simply by looking at the degree of the polynomial.