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

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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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
First let y=0

x%5E2%2Bx-6=0

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


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve x%5E2%2Bx-6=0 ( notice a=1, b=1, and c=-6)

x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A1%2A-6+%29%29%2F%282%2A1%29 Plug in a=1, b=1, and c=-6



x+=+%28-1+%2B-+sqrt%28+1-4%2A1%2A-6+%29%29%2F%282%2A1%29 Square 1 to get 1



x+=+%28-1+%2B-+sqrt%28+1%2B24+%29%29%2F%282%2A1%29 Multiply -4%2A-6%2A1 to get 24



x+=+%28-1+%2B-+sqrt%28+25+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-1+%2B-+5%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-1+%2B-+5%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-1+%2B+5%29%2F2 or x+=+%28-1+-+5%29%2F2

Lets look at the first part:

x=%28-1+%2B+5%29%2F2

x=4%2F2 Add the terms in the numerator
x=2 Divide

So one answer is
x=2



Now lets look at the second part:

x=%28-1+-+5%29%2F2

x=-6%2F2 Subtract the terms in the numerator
x=-3 Divide

So another answer is
x=-3

So our solutions are:
x=2 or x=-3

Notice when we graph x%5E2%2Bx-6, we get:

+graph%28+500%2C+500%2C+-13%2C+12%2C+-13%2C+12%2C1%2Ax%5E2%2B1%2Ax%2B-6%29+

and we can see that the roots are x=2 and x=-3. This verifies our answer