SOLUTION: Find the values of p for which the graph of y=px^2+8x+p-6y crosses the x-axis.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Find the values of p for which the graph of y=px^2+8x+p-6y crosses the x-axis.      Log On


   



Question 1019659: Find the values of p for which the graph of
y=px^2+8x+p-6y
crosses the x-axis.

Found 2 solutions by stanbon, KMST:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the values of p for which the graph of
y=px^2+8x+p-6y
crosses the x-axis.
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Did you post that correctly??

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
It is strange to have y on both sides of the equal sign.
If you did post correctly,
y=px%5E2%2B8x%2Bp-6y
y%2B6y=px%5E2%2B8x%2Bp
7y=px%5E2%2B8x%2Bp<-->y=%28px%5E2%2B8x%2Bp%29%2F7<-->y=%28p%2F7%29x%5E2%2B%288%2F7%29x%2Bp%2F7
If the graph of that quadratic function crosses the y=0%7D%7D+x-axis%2C%0D%0Ait+will+do+it+at+two+values+of+%7B%7B%7Bx ,
meaning that y=0 will give two distinct solutions for x .
That means px%5E2%2B8x%2Bp=0 has two distinct solutions for x .
If a quadratic equation ax%5E2%2Bbx%2Bc=0 has two distinct solutions for x ,
it means that the discriminant is positive:
b%5E2-4ac%3E0 .
In this case, that would be
8%5E2-4%2Ap%2Ap%3E0
64-4p%5E2%3E0
16-p%5E2%3E0
16%3Ep%5E2
highlight%28-4%3Cp%3C4%29