SOLUTION: Select the approximate values of x that are solutions to f(x) = 0, where f(x) = -3x2 + 2x + 8. 1.{-1.33,2.00} 2.{-3,2} 3.{-0.67,-2.67} 4.{-0.38,0.25}

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Select the approximate values of x that are solutions to f(x) = 0, where f(x) = -3x2 + 2x + 8. 1.{-1.33,2.00} 2.{-3,2} 3.{-0.67,-2.67} 4.{-0.38,0.25}      Log On


   

Question 878617: Select the approximate values of x that are solutions to f(x) = 0, where
f(x) = -3x2 + 2x + 8.
1.{-1.33,2.00}
2.{-3,2}
3.{-0.67,-2.67}
4.{-0.38,0.25}
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

f(x) = -3x2 + 2x + 8.

 1.{-1.33,2.00}

 


 
Solved by pluggable solver: SOLVE quadratic equation with variable


Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -3x%5E2%2B2x%2B8+=+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%2A-3%2A8=100.

  

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

  

    x%5B1%5D+=+%28-%282%29%2Bsqrt%28+100+%29%29%2F2%5C-3+=+-1.33333333333333

    x%5B2%5D+=+%28-%282%29-sqrt%28+100+%29%29%2F2%5C-3+=+2

    

    Quadratic expression -3x%5E2%2B2x%2B8 can be factored:

  -3x%5E2%2B2x%2B8+=+-3%28x--1.33333333333333%29%2A%28x-2%29

  Again, the answer is: -1.33333333333333, 2.
Here's your graph:

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-3%2Ax%5E2%2B2%2Ax%2B8+%29