SOLUTION: When are there two solutions in quadratic equations???

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: When are there two solutions in quadratic equations???      Log On


   



Question 2823: When are there two solutions in quadratic equations???
Found 2 solutions by AnlytcPhil, WannabeCAgirl83:
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
>>When are there two solutions in quadratic equations???<<
`
Every quadratic equation

ax%5E2+%2B+bx+%2B+c+=+0

has either

1. Two real solutions
2. One real solution
3. Two conjugate imaginary solutions

The quadratic equation:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+  

has two real solutions when the " ± " part gives two different 
answers, one for the + and another for the -.  This will always 
be the case when the radicand, or "discriminant",

b%5E2+-+4ac¹0 

If 

b%5E2+-+4ac > 0, the two solutions are real, and when

b%5E2+-+4ac < 0, the two solutions are conjugate imaginary
numbers.

However, if 

b%5E2+-+4ac = 0, there is but one real solution, because the
"±" part is "±0", and whether we add 0 or subtract 0, we still 
get the same number.

Edwin J

Answer by WannabeCAgirl83(35) About Me  (Show Source):
You can put this solution on YOUR website!
In quadratic equations, what matters is the value of discriminant b%5E2-4ac. If it is positive, there are 2 solutions. You can't get a root from negative discriminants. In that case there is no solution. If the discriminant is zero, there is one solution.