SOLUTION: I am doing quadratic equations, the problem is {{{ X^2-x-12 }}} I understand most of it except for when I get to where the problem says x = -1 sqrt(47)/2 I don't know what to do wi

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I am doing quadratic equations, the problem is {{{ X^2-x-12 }}} I understand most of it except for when I get to where the problem says x = -1 sqrt(47)/2 I don't know what to do wi      Log On


   

Question 366738: I am doing quadratic equations, the problem is +X%5E2-x-12+ I understand most of it except for when I get to where the problem says x = -1 sqrt(47)/2 I don't know what to do with the square root symbol. I know how to find the vertex but I don't have the roots to graph the parabola, If some one could help me with this I would be grateful.
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
You didn't show an equation. All equations have an equal sign.
If you mean x%5E2+-+x+-+12+=+0 you missed a sign somewhere, it's sqrt(49).
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%2B-12+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-1%29%5E2-4%2A1%2A-12=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+49+%29%29%2F2%5C1+=+4
x%5B2%5D+=+%28-%28-1%29-sqrt%28+49+%29%29%2F2%5C1+=+-3

Quadratic expression 1x%5E2%2B-1x%2B-12 can be factored:
1x%5E2%2B-1x%2B-12+=+%28x-4%29%2A%28x--3%29
Again, the answer is: 4, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B-12+%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-x-12=0 Start with the given equation.


Notice that the quadratic x%5E2-x-12 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-1, and C=-12


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%28-12%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-1, and C=-12


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%28-12%29+%29%29%2F%282%281%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%281%29%28-12%29+%29%29%2F%282%281%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1--48+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-12%29 to get -48


x+=+%281+%2B-+sqrt%28+1%2B48+%29%29%2F%282%281%29%29 Rewrite sqrt%281--48%29 as sqrt%281%2B48%29


x+=+%281+%2B-+sqrt%28+49+%29%29%2F%282%281%29%29 Add 1 to 48 to get 49. This is probably where you made your mistake.


x+=+%281+%2B-+sqrt%28+49+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%281+%2B-+7%29%2F%282%29 Take the square root of 49 to get 7.


x+=+%281+%2B+7%29%2F%282%29 or x+=+%281+-+7%29%2F%282%29 Break up the expression.


x+=+%288%29%2F%282%29 or x+=++%28-6%29%2F%282%29 Combine like terms.


x+=+4 or x+=+-3 Simplify.


So the solutions are x+=+4 or x+=+-3

So the roots (or x-intercepts) are (4,0) and (-3,0)