How to use the discriminant to find out what type of solutions the equation has for #2m^2 - m - 6 = 0#?

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Answer 1 · 2015-05-25T21:43:18

#2m^2-m-6# is of the form #am^2+bm+c#, with #a=2#, #b=-1# and #c=-6#.

The discriminant is given by the formula:

#Delta = b^2-4ac#

#= (-1)^2 - (4xx2xx-6) = 1+48 = 49 = 7^2#

#Delta > 0# so the equation #2m^2-m-6=0# has two distinct real roots.

In addition, it is a perfect square, so those roots are rational.

The roots are given by the formula:

#m = (-b+-sqrt(Delta))/(2a) = (1+-7)/4#

That is #m=-3/2# and #m=2#