SOLUTION: 8. Use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. Determine the number and types of solutions.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 8. Use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. Determine the number and types of solutions.       Log On


   

Question 187211: 8. Use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. Determine the number and types of solutions.
(3)^1/2y^2 - 4y - 7(3)^1/2 = 0
this is as difficult as it looks. I know. I've tried. Any assistance would be greatly appreciated. Thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Take note that sqrt%283%29%2Ay%5E2-4y-7%2Asqrt%283%29 is in ay%5E2%2Bby%2Bc form.


So from sqrt%283%29%2Ay%5E2-4y-7%2Asqrt%283%29 we can see that a=sqrt%283%29, b=-4, and c=-7%2Asqrt%283%29


Now let's use the discriminant D=b%5E2-4ac to find the number and type of solutions:


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


D=%28-4%29%5E2-4%28sqrt%283%29%29%28-7%2Asqrt%283%29%29 Plug in a=sqrt%283%29, b=-4, and c=-7%2Asqrt%283%29


D=16-4%28sqrt%283%29%29%28-7%2Asqrt%283%29%29 Square -4 to get %28-4%29%5E2=%28-4%29%28-4%29=16


D=16-%284%29%28-7%29%28sqrt%283%29%2Asqrt%283%29%29 Rearrange the terms.


D=16%2B28%2Asqrt%283%29%2Asqrt%283%29 Multiply -4 and -7 to get 28


D=16%2B28%283%29 Multiply sqrt%283%29 and sqrt%283%29 to get sqrt%283%29%2Asqrt%283%29=%28sqrt%283%29%29%5E2=3


D=16%2B84 Multiply


D=100 Add

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