SOLUTION: can you please help me solve the following: (((In the equation ax^2+bx+c=0, the value of b^2-4ac is called the___________of the quardratic equation. What does this value tell you a

Algebra ->  Expressions-with-variables -> SOLUTION: can you please help me solve the following: (((In the equation ax^2+bx+c=0, the value of b^2-4ac is called the___________of the quardratic equation. What does this value tell you a      Log On


   

Question 180346This question is from textbook algebra structure and method
: can you please help me solve the following: (((In the equation ax^2+bx+c=0, the value of b^2-4ac is called the___________of the quardratic equation. What does this value tell you about the real roots of the equation?))) This question is from textbook algebra structure and method

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
can you please help me solve the following: (((In the equation ax^2+bx+c=0, the value of b^2-4ac is called the___________of the quardratic equation. What does this value tell you about the real roots of the equation?)))
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This is well explained in the on site solver. I'll submit an example eqn.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%2B-6+=+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%2A1%2A-6=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+25+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+25+%29%29%2F2%5C1+=+3
x%5B2%5D+=+%28-%28-1%29-sqrt%28+25+%29%29%2F2%5C1+=+-2

Quadratic expression 1x%5E2%2B-1x%2B-6 can be factored:
1x%5E2%2B-1x%2B-6+=+%28x-3%29%2A%28x--2%29
Again, the answer is: 3, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B-6+%29