SOLUTION: For the following equation, state the value of the discriminant and then describe the nature of the solutions. 2x^2-10x-12=0 What is the value of the discriminant? Which o

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: For the following equation, state the value of the discriminant and then describe the nature of the solutions. 2x^2-10x-12=0 What is the value of the discriminant? Which o      Log On


   

Question 244806: For the following equation, state the value of the discriminant and then describe the nature of the solutions.
2x^2-10x-12=0
What is the value of the discriminant?
Which one of the statements below is correct?
a. The equation has two imaginary solutions.
b. The equation has two real solutions.
c. The equation has one real solution?
Thanks for your help!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

From 2x%5E2-10x-12 we can see that a=2, b=-10, and c=-12


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


D=%28-10%29%5E2-4%282%29%28-12%29 Plug in a=2, b=-10, and c=-12


D=100-4%282%29%28-12%29 Square -10 to get 100


D=100--96 Multiply 4%282%29%28-12%29 to get %288%29%28-12%29=-96


D=100%2B96 Rewrite D=100--96 as D=100%2B96


D=196 Add 100 to 96 to get 196


Since the discriminant is greater than zero, this means that there are two real solutions.