Question 119096
 From the quadratic formula

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}


the discriminant consists of all of the terms in the square root. So the discriminant is


{{{D=b^2-4ac}}}


the discriminant tells us how many solutions (and what type of solutions) we can expect for any quadratic. 



So let's find the discriminant for {{{px^2 + (2p+1)x+p}}}



{{{D=(2p+1)^2-4*p*p}}} Plug in {{{a=p}}}, {{{b=2p+1}}}, {{{c=p}}}


{{{D=4p^2+4p+1-4p^2}}} Foil and multiply


{{{D=4p+1}}} Combine like terms




Now since we want to have 2 non-real solutions, this means {{{D<0}}}



{{{3p+1<0}}} Set the discriminant less than zero




{{{4p<0-1}}}Subtract 1 from both sides



{{{4p<-1}}} Combine like terms on the right side



{{{p<(-1)/(4)}}} Divide both sides by 4 to isolate p 




{{{p<-1/4}}} Reduce


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Answer:

So our answer is {{{p<-1/4}}}  (which is approximately {{{p<-0.25}}} in decimal form)




So you're on the right track, but you have to remember that values such as {{{p=-10}}} work also since -10 is less than {{{-1/4}}}