SOLUTION: Add the following polynomials: (1/5x^2-1/5x-3/4)+(1/10x^2-1/2x+1/2)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Add the following polynomials: (1/5x^2-1/5x-3/4)+(1/10x^2-1/2x+1/2)      Log On


   

Question 607660: Add the following polynomials:
(1/5x^2-1/5x-3/4)+(1/10x^2-1/2x+1/2)
Answer by jerryguo41(197) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F5x%5E2-1%2F5x-3%2F4%29%2B%281%2F10x%5E2-1%2F2x%2B1%2F2%29
%281%2F5%29x%5E2%2B%281%2F10%29x%5E2-%281%2F5%29x-%281%2F2%29x-%283%2F4%29%2B%281%2F2%29
%283%2F5%29x%5E2-%287%2F10%29x-%281%2F2%29
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 0.6x%5E2%2B-0.7x%2B-0.5+=+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=%28-0.7%29%5E2-4%2A0.6%2A-0.5=1.69.

Discriminant d=1.69 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--0.7%2B-sqrt%28+1.69+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-0.7%29%2Bsqrt%28+1.69+%29%29%2F2%5C0.6+=+1.66666666666667
x%5B2%5D+=+%28-%28-0.7%29-sqrt%28+1.69+%29%29%2F2%5C0.6+=+-0.5

Quadratic expression 0.6x%5E2%2B-0.7x%2B-0.5 can be factored:
0.6x%5E2%2B-0.7x%2B-0.5+=+0.6%28x-1.66666666666667%29%2A%28x--0.5%29
Again, the answer is: 1.66666666666667, -0.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.6%2Ax%5E2%2B-0.7%2Ax%2B-0.5+%29