Question

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

Answer 1

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`