SOLUTION: Use the following quadratic equation to complete parts a and b below. You must show all work. x2 + 4x - 21 = 0 a. Solve by factoring. b. Solve using the quadratic formula

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Use the following quadratic equation to complete parts a and b below. You must show all work. x2 + 4x - 21 = 0 a. Solve by factoring. b. Solve using the quadratic formula      Log On


   

Question 310094: Use the following quadratic equation to complete parts a and b below. You must show all work.
x2 + 4x - 21 = 0
a. Solve by factoring.
b. Solve using the quadratic formula
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Use the following quadratic equation to complete parts a and b below. You must show all work.
x2 + 4x - 21 = 0
a. Solve by factoring.
(x+7)*(x-3) = 0
x = -7, 3
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b. Solve using the quadratic formula
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B-21+=+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=%284%29%5E2-4%2A1%2A-21=100.

Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+100+%29%29%2F2%5C1+=+3
x%5B2%5D+=+%28-%284%29-sqrt%28+100+%29%29%2F2%5C1+=+-7

Quadratic expression 1x%5E2%2B4x%2B-21 can be factored:
1x%5E2%2B4x%2B-21+=+%28x-3%29%2A%28x--7%29
Again, the answer is: 3, -7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-21+%29