SOLUTION: f(x) = 3x^+2x-4

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Question 32937: f(x) = 3x^+2x-4
Answer by xcentaur(357) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=3x^+2x-4
equate f(x)=0 to get the roots
now
3x^+2x-4=0
this is a quadratic in x
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B2x%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=%282%29%5E2-4%2A3%2A-4=52.

Discriminant d=52 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+52+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+52+%29%29%2F2%5C3+=+0.86851709182133
x%5B2%5D+=+%28-%282%29-sqrt%28+52+%29%29%2F2%5C3+=+-1.535183758488

Quadratic expression 3x%5E2%2B2x%2B-4 can be factored:
3x%5E2%2B2x%2B-4+=+%28x-0.86851709182133%29%2A%28x--1.535183758488%29
Again, the answer is: 0.86851709182133, -1.535183758488. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B2%2Ax%2B-4+%29


So you have your 2 values of x


If you were looking for the domain and range for the function f(x),please post again,clearly stating the question
Hope this helps,
xC