SOLUTION: I am having a problem with this problem, Find the x-intercepts Y=x^2+x-6 Thanks a million

Question 91979: I am having a problem with this problem,
Find the x-intercepts
Y=x^2+x-6
Thanks a million
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the x-intercepts
Y=x^2+x-6
---------
Let y=0 then:
x^2+x-6=0
(x+3)(x-2)=0
x=-3 or x=2
===================
Cheers,
Stan H.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First let y=0

Now let's use the quadratic formula to find the x-intercepts:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=1, and c=-6

Square 1 to get 1

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or

Notice when we graph , we get:

and we can see that the roots are and . This verifies our answer
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