SOLUTION: Can anyone help? Unit 2 Discussion Board Deliverable Length: 3 - 4 paragraphs Details: When using the quadratic formula to solve a quadratic equation ax2 + bx + c = 0, the d

Algebra ->  Graphs -> SOLUTION: Can anyone help? Unit 2 Discussion Board Deliverable Length: 3 - 4 paragraphs Details: When using the quadratic formula to solve a quadratic equation ax2 + bx + c = 0, the d      Log On


   

Question 48236: Can anyone help?
Unit 2 Discussion Board
Deliverable Length: 3 - 4 paragraphs
Details: When using the quadratic formula to solve a quadratic equation ax2 + bx + c = 0, the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. (When the discriminant is negative, then we have the square root of a negative number. This is called an imaginary number, sqrt(-1) = i. )
Explain what the value of the discriminant means to the graph of y = ax2 + bx + c. Hint: Chose values of a, b and c to create a particular discriminant. Then, graph the corresponding equation.
Search the Cybrary and Internet. In the real world, where might these imaginary numbers be used?

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Let a=1, b=2, and c=3 to get:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B3+=+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=%282%29%5E2-4%2A1%2A3=-8.

The discriminant -8 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -8 is + or - sqrt%28+8%29+=+2.82842712474619.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B3+%29

Imaginary numbers are part of the Complex Number System
One use for them is found in electronics. You might
try Google to search for applications of imaginary numbers.
Cheers,
Stan H.