Discriminant

Question

find exact values of p if

px^2 - 2x + 3p = 0 is a negative definite

I have the process to get the answer-

p < - 1/√3

Answer 1

I'm confused by the wording of your question but I'll try to help

 

My questions for you:

 

1) The words "negative definite" - did you mean "negative discriminant"

 

2) you ended your message with "p < - 1/√3"

 

This is one possible answer. Why did you put only this?

 

Here's the problem worked 

 

If px² - 2x + 3p =0 is your quadratic then a =p, b = -2 and c = 3p

The discriminant is defined as b² - 4ac

 

Plug in for a, b, and c

 

(-2)²- 4(p)(3p) < 0

 

4 - 12p² < 0

 

-12p² < -4    The next step is to divide by -12. This will change the direction of the inequality symbol.

 

p² > 1/3   Now there are two sets of numbers that satisfy this inequality

 

The first is  :   p >1/√3 which is the same as saying p > √3/3

The second is : p <- 1/√3  also written p < -√3/3

 

I can't say if both the first and second are the answers until I hear back from you about my questions.

 

 

 

 

Answer 2

(-2)^2 - 4*p*(3p) < 0

 4 - 12p^2 < 0

 

 1 - 3p^2 <0

 

 1 < 3p^2

 

1/3 < p^2

 

1/sqrt(3) < p

 

sqrt(3)/3 < p