SOLUTION: Evaluate the discriminant of each equation. How many real and imaginary soulutions does each have? if you could help with the 4 problems i can do the rest of the paper please expla

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Evaluate the discriminant of each equation. How many real and imaginary soulutions does each have? if you could help with the 4 problems i can do the rest of the paper please expla      Log On


   

Question 259866: Evaluate the discriminant of each equation. How many real and imaginary soulutions does each have? if you could help with the 4 problems i can do the rest of the paper please explain as well so i can see what im doing please
x^2+5x+6=0
3x^2-4x+3=0
-2x^2-5x+4=0
16x^2-8x+1=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you going

# 1


From x%5E2%2B5x%2B6 we can see that a=1, b=5, and c=6


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


D=%285%29%5E2-4%281%29%286%29 Plug in a=1, b=5, and c=6


D=25-4%281%29%286%29 Square 5 to get 25


D=25-24 Multiply 4%281%29%286%29 to get %284%29%286%29=24


D=1 Subtract 24 from 25 to get 1


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

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# 2


From 3x%5E2-4x%2B3 we can see that a=3, b=-4, and c=3


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


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


D=16-4%283%29%283%29 Square -4 to get 16


D=16-36 Multiply 4%283%29%283%29 to get %2812%29%283%29=36


D=-20 Subtract 36 from 16 to get -20


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


In other words, there are no real solutions.