SOLUTION: For the following equation, state the value of the discriminant and then describe the nature of the solutions. 13x^2+8x+3=0 What is the value of the discriminant? Which one o

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: For the following equation, state the value of the discriminant and then describe the nature of the solutions. 13x^2+8x+3=0 What is the value of the discriminant? Which one o      Log On


   

Question 503480: For the following equation, state the value of the discriminant and then describe the nature of the solutions.
13x^2+8x+3=0
What is the value of the discriminant?
Which one of the statements below is correct?
a. The equation has two real solutions.
b. The equation has one real solution.
c. the equation has two imaginary solutions
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
13x^2+8x+3=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 13x%5E2%2B8x%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=%288%29%5E2-4%2A13%2A3=-92.

The discriminant -92 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 -92 is + or - sqrt%28+92%29+=+9.59166304662544.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+13%2Ax%5E2%2B8%2Ax%2B3+%29