SOLUTION: I am trying to help my daughter witht his quadractic equation. She has to find the root of the quadratic equation in standard form. y=x^2+7x+12 It has been a long time since I've

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I am trying to help my daughter witht his quadractic equation. She has to find the root of the quadratic equation in standard form. y=x^2+7x+12 It has been a long time since I've       Log On


   

Question 432871: I am trying to help my daughter witht his quadractic equation. She has to find the root of the quadratic equation in standard form. y=x^2+7x+12 It has been a long time since I've done this and I need direction to be able to help her with the rest of the problems. Any help would be appreciated!
Found 2 solutions by mananth, Alan3354:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
x^2+7x+12
Split the middle term into two such that when the parts are added the give 7x and when multiplied give the product of the first & last term.
x^2+4x+3x+12
x(x+4)+3(x+4)
(x+4)(x+3)
x=-4 ,x=-3

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
find the root of the quadratic equation in standard form.
y=x^2+7x+12
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You can factor it
y=x^2+7x+12 = 0
(x+3)*(x+4) = 0
x = -3, -4
Or use the quadratic equation.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B7x%2B12+=+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=%287%29%5E2-4%2A1%2A12=1.

Discriminant d=1 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+1+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+1+%29%29%2F2%5C1+=+-3
x%5B2%5D+=+%28-%287%29-sqrt%28+1+%29%29%2F2%5C1+=+-4

Quadratic expression 1x%5E2%2B7x%2B12 can be factored:
1x%5E2%2B7x%2B12+=+%28x--3%29%2A%28x--4%29
Again, the answer is: -3, -4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B7%2Ax%2B12+%29