SOLUTION: Plot the graph of y= x3- 1.5x2- 8.5x +4.5 from x= -4 to x= +4 at 1 unit intervals, and use the graph to solve the cubic equation x³-1.5x2 -8.5x + 4.5= 0

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Plot the graph of y= x3- 1.5x2- 8.5x +4.5 from x= -4 to x= +4 at 1 unit intervals, and use the graph to solve the cubic equation x³-1.5x2 -8.5x + 4.5= 0      Log On


   

Question 189342: Plot the graph of y= x3- 1.5x2- 8.5x +4.5 from x= -4 to x= +4 at 1 unit intervals, and use the graph to solve the cubic equation x³-1.5x2 -8.5x + 4.5= 0
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Plot the graph of y= x3- 1.5x2- 8.5x +4.5 from x= -4 to x= +4 at 1 unit intervals, and use the graph to solve the equation x³-1.5x2 -8.5x + 4.5= 0
-----------------------
I did that. I use the graphing software from www.padowan.dk.com/graph/ (it's free)
I suspected that 0.5 is a zero because of the fractions in the equation, and it is.
Multiply the eqn by 2, then, after dividing by (x-1) you have
2x^2 - x - 18 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-1x%2B-18+=+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=%28-1%29%5E2-4%2A2%2A-18=145.

Discriminant d=145 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+145+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+145+%29%29%2F2%5C2+=+3.26039864469807
x%5B2%5D+=+%28-%28-1%29-sqrt%28+145+%29%29%2F2%5C2+=+-2.76039864469807

Quadratic expression 2x%5E2%2B-1x%2B-18 can be factored:
2x%5E2%2B-1x%2B-18+=+%28x-3.26039864469807%29%2A%28x--2.76039864469807%29
Again, the answer is: 3.26039864469807, -2.76039864469807. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-1%2Ax%2B-18+%29