SOLUTION: Hiiii,, Could you please help me about this?!I solved it but the answers was undefined!!!!Also could you tell me what is the discriminant?Thanksss By examination of the discrimina

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hiiii,, Could you please help me about this?!I solved it but the answers was undefined!!!!Also could you tell me what is the discriminant?Thanksss By examination of the discrimina      Log On


   

Question 201986: Hiiii,, Could you please help me about this?!I solved it but the answers was undefined!!!!Also could you tell me what is the discriminant?Thanksss
By examination of the discriminant, determine the nature of the roots for the following equation:
7x%5E2%2B10x%2B5=0
Found 2 solutions by vleith, jim_thompson5910:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 7x%5E2%2B10x%2B5+=+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=%2810%29%5E2-4%2A7%2A5=-40.

The discriminant -40 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 -40 is + or - sqrt%28+40%29+=+6.32455532033676.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+7%2Ax%5E2%2B10%2Ax%2B5+%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

From 7x%5E2%2B10x%2B5 we can see that a=7, b=10, and c=5


D=b%5E2-4ac Start with the discriminant formula.


D=%2810%29%5E2-4%287%29%285%29 Plug in a=7, b=10, and c=5


D=100-4%287%29%285%29 Square 10 to get 100


D=100-140 Multiply 4%287%29%285%29 to get %2828%29%285%29=140


D=-40 Subtract 140 from 100 to get -40


Since the discriminant is less than zero, this means that there are two complex solutions.


In other words, there are no real solutions.