SOLUTION: 3K SQUARED+7K=4 TEXTBOOK: ISBN 0-321-12711-0

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Question 64014This question is from textbook
: 3K SQUARED+7K=4
TEXTBOOK: ISBN 0-321-12711-0 This question is from textbook

Answer by sarahschober(35) About Me  (Show Source):
You can put this solution on YOUR website!
Just substitute k for x
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B7x%2B-4+=+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%2A3%2A-4=97.

Discriminant d=97 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+97+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+97+%29%29%2F2%5C3+=+0.474809633632684
x%5B2%5D+=+%28-%287%29-sqrt%28+97+%29%29%2F2%5C3+=+-2.80814296696602

Quadratic expression 3x%5E2%2B7x%2B-4 can be factored:
3x%5E2%2B7x%2B-4+=+%28x-0.474809633632684%29%2A%28x--2.80814296696602%29
Again, the answer is: 0.474809633632684, -2.80814296696602. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B7%2Ax%2B-4+%29