SOLUTION: In this question I need to use the “discriminant” to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. I need help please!

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: In this question I need to use the “discriminant” to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. I need help please!      Log On


   

Question 144828: In this question I need to use the “discriminant” to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. I need help please!!
3. 3z2 + z - 1 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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


From 3z%5E2%2Bz-1 we can see that a=3, b=1, and c=-1


D=%281%29%5E2-4%283%29%28-1%29 Plug in a=3, b=1, and c=-1


D=1-4%283%29%28-1%29 Square 1 to get 1


D=1--12 Multiply 4%283%29%28-1%29 to get %2812%29%28-1%29=-12


D=1%2B12 Rewrite D=1--12 as D=1%2B12


D=13 Add 1 to 12 to get 13


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