SOLUTION: Help! I asked earlier and I have tried but I do not even understand the question. Can someone please help me understand these two? Determine the nature of the solutions of the equ

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Help! I asked earlier and I have tried but I do not even understand the question. Can someone please help me understand these two? Determine the nature of the solutions of the equ      Log On


   

Question 469064: Help! I asked earlier and I have tried but I do not even understand the question. Can someone please help me understand these two?
Determine the nature of the solutions of the equations.
y^2=1/5y+2/3
x^2-4=0
Is there one real solution, two real solutions, or two non real solutions?
I believe that the first one has 2 real solutions and that the second one has two non real solutions. Did I even come close?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Determine the nature of the solutions of the equations.
y^2=1/5y+2/3
x^2-4=0
:
You do this by using the rules of the discriminant
:
The equation should be in the form ax^2 + bx + c
:
The discriminant: d = b^2 - 4*a*c
The rules,
If d > 0 there are two distinct real roots (solutions)
If d = 0 there is one real solution(a double root)
If d < 0 there is two imaginary roots, one the conjugate of the other
:
Put the 1st equation in ax^2 + bx + c form
y^2 - 1%2F5y - 2%2F3
then
a=1
b=-1%2F5
c=-2%2F3
d = %28-1%2F5%29%5E2 - 4 * 1 * -2%2F3
d = 1%2F25 - -8%2F3
which is
d = 1%2F25 + 8%2F3
d > 0, therefore there are two distinct real roots, (the exact value is not needed) so you are right.
:
the 2nd equation is in ax^2 + bx + c form
x^2 - 4 = 0
a=1
b=0
c=-4
d = -4*1*-4
d = +16 > 0, also two distinct real roots
:
You can see that if you solve it
x^2 -4 = 0
x^2 = 4
x = +/-sqrt%284%29
x = +2
and
x = -2