SOLUTION: If {{{f(x)=4x^2+7x+2}}} Find the following: f(x)<0 f(x)>0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: If {{{f(x)=4x^2+7x+2}}} Find the following: f(x)<0 f(x)>0      Log On


   

Question 273993: If f%28x%29=4x%5E2%2B7x%2B2
Find the following:
f(x)<0


f(x)>0
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=4x^2+7x+2
4x^2+7x+2=0
x=(-7-sqrt(17))/8, x=(-7+sqrt(17)) see below
f(x)<0 ((-7-sqrt(17))/8) f(x)>0 ((-7-sqrt(17))/8)>x>((-7+sqrt(17))/8)
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Ed
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B7x%2B2+=+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%2A4%2A2=17.

Discriminant d=17 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+17+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+17+%29%29%2F2%5C4+=+-0.359611796797792
x%5B2%5D+=+%28-%287%29-sqrt%28+17+%29%29%2F2%5C4+=+-1.39038820320221

Quadratic expression 4x%5E2%2B7x%2B2 can be factored:
4x%5E2%2B7x%2B2+=+4%28x--0.359611796797792%29%2A%28x--1.39038820320221%29
Again, the answer is: -0.359611796797792, -1.39038820320221. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B7%2Ax%2B2+%29