SOLUTION: What values of "a" does the function f(x)=ax^2+6x+9 have two zeros, have one zero, have no zero's thank you :)

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: What values of "a" does the function f(x)=ax^2+6x+9 have two zeros, have one zero, have no zero's thank you :)      Log On


   

Question 1038671: What values of "a" does the function f(x)=ax^2+6x+9 have two zeros, have one zero, have no zero's
thank you :)
Found 3 solutions by josgarithmetic, MathTherapy, Alan3354:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
6%5E2-4%2Aa%2A9
36-36a------discriminant.

Notice that if a=1, f is a perfect square and f%28x%29=%28x%2B3%29%5E2 and has exactly ONE zero.


a%3C1 ------------ two real zeros

a%3E1 ------------ No real zeros

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

What values of "a" does the function f(x)=ax^2+6x+9 have two zeros, have one zero, have no zero's
thank you :)
Two zeroes:matrix%281%2C5%2C+Discriminant%2C+or%2C+b%5E2+-+4ac%2C+%22%3E%22%2C+0%29

One zero:  matrix%281%2C5%2C+Discriminant%2C+or%2C+b%5E2+-+4ac%2C+%22=%22%2C+0%29

No zeroes: matrix%281%2C5%2C+Discriminant%2C+or%2C+b%5E2+-+4ac%2C+%22%3C%22%2C+0%29

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
All quadratics have 2 zeroes.
If you mean real zeroes, you should say that.