SOLUTION: (48x^5+24x^4-18x^3)/(6x^2)

Algebra ->  Finance -> SOLUTION: (48x^5+24x^4-18x^3)/(6x^2)      Log On


   

Question 352551: (48x^5+24x^4-18x^3)/(6x^2)
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Here is a link to help with long division.
http://www.calc101.com/webMathematica/long-divide.jsp#topdoit
But this problem can be solved by factoring
%2848x%5E5%2B24x%5E4-18x%5E3%29%2F%286x%5E2%29
%28%286x%5E2%29%288x%5E3+%2B+4x%5E2+-+3x%29%29%2F%286x%5E2%29
%288x%5E3+%2B+4x%5E2+-+3x%29
x%288x%5E2+%2B+4x+-+3%29
You can further factor the quadractic using the quadratic equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 8x%5E2%2B4x%2B-3+=+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=%284%29%5E2-4%2A8%2A-3=112.

Discriminant d=112 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+112+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+112+%29%29%2F2%5C8+=+0.411437827766148
x%5B2%5D+=+%28-%284%29-sqrt%28+112+%29%29%2F2%5C8+=+-0.911437827766148

Quadratic expression 8x%5E2%2B4x%2B-3 can be factored:
8x%5E2%2B4x%2B-3+=+8%28x-0.411437827766148%29%2A%28x--0.911437827766148%29
Again, the answer is: 0.411437827766148, -0.911437827766148. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B4%2Ax%2B-3+%29