How do you use the discriminant to determine the nature of the solutions given # –3p^2 – p + 2 = 0#?

1 Answer
Aug 26, 2016

Answer:

As the discriminant is positive the nature of the solutions are such that the graph crosses the x-axis so #x in RR# for #-3p^2-p+2=0#

Explanation:

Standard for equation but with #p# instead of #x#:#->ap^2-p+2=0#

where a = -3; b= -1; c=+2

#=>p=(-b+-sqrt(b^2-4ac))/(2a)#

Thus the discriminant #b^2-4ac" "->" "(-3)^2-4(-3)(+2)= +33#

The nature if the solution is that the plot does cross the x-axis. So there are values of #x# where #-3p^2-p+2=0# is true

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By the way. If the coefficient of #x^2# is positive then the graph is of general shape #uu#.

However, the coefficient is -3 thus negative. So the graph is of general shape #nn#