SOLUTION: For what Values of p will the expression p+8x-3x^2 always be positive?

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Question 84466: For what Values of p will the expression p+8x-3x^2 always be positive?
Found 2 solutions by venugopalramana, ikleyn:
Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website!
For what Values of p will the expression p+8x-3x^2 always be positive?
FOR NO VALUE OF P WILL IT BE ALWAYS POSITIVE.
QUADRATIC WILL ALWAYS HAVE ONE SIGN POSITIVE OR NEGATIVE IF ITS
DISCRIMINANT IS NEGATIVE.
THEN IT WILL ALWAYS BE +VE IF COEFFICIENT OF X^2 IS POSITIVE
OR IT WILL ALWAYS BE - VE. IF COEFFICIENT OF X^2 IS NEGATIVE,AS
IS THE CASE HERE.HENCE IF
D=8^2-4P(-3)<0...THAT IS 64-12P<0...THAT IS....P>64/12=16/3,THE FUNCTION WILL BE ALWAYS NEGATIVE.

Answer by ikleyn(54060) (Show Source):
You can put this solution on YOUR website!
.
For what Values of p will the expression p+8x-3x^2 always be positive?
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As worded in the post, the given quadratic function has a negative leading coefficient.

This means the corresponding parabolas are all open downward. They extend downwards infinitely.

Hence, such a value of 'p' that would make p+8x-3x^2 always positive DOES NOT EXIST.

So, the problem is either a TRAP or is worded incorrectly (like a sock put on inside out).