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

1 Answer
Tony B
Aug 26, 2016

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

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