SOLUTION: Determine the number of solutions of 2x^2 - 3x - 5 = 0

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Question 258053: Determine the number of solutions of 2x^2 - 3x - 5 = 0
Answer by Greenfinch(383) About Me  (Show Source):
You can put this solution on YOUR website!
The discriminant is 9 + 4x4x5 = 49
So 2 answers to 2X^2 - 3x -5 =0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-3x%2B-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=%28-3%29%5E2-4%2A2%2A-5=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+49+%29%29%2F2%5C2+=+2.5
x%5B2%5D+=+%28-%28-3%29-sqrt%28+49+%29%29%2F2%5C2+=+-1

Quadratic expression 2x%5E2%2B-3x%2B-5 can be factored:
2x%5E2%2B-3x%2B-5+=+2%28x-2.5%29%2A%28x--1%29
Again, the answer is: 2.5, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-3%2Ax%2B-5+%29