How do use the discriminant to find all values of c for which the equation #2x^2-x-c=0# has two real roots?

1 Answer
Apr 3, 2017

Answer:

You first write out the discriminant #D=b^2-4ac#

Explanation:

We know the values of #a# and #b#, so:
#D=(-1)^2-4*2*(-c)=1+8c#

For two (unequal) real roots #D>0#, or:
#1+8c>0->8c> -1->c> -1/8#

Below is the graph of the borderline case, where #D=0#, and the parabole will be #2x^2-x-(-1/8)#
graph{2x^2-x+1/8 [-10, 10, -5, 5]}

You will see, that as #c> -1/8# the parabole will sink.
Here #c=+1# so the parabole will be #2x^2-x-(+1)#
graph{2x^2-x-1 [-10, 10, -5, 5]}