How to use the discriminant to find out how many real number roots an equation has for #2m^2 - m - 6 = 0#?

1 Answer
Mar 26, 2018

Answer:

See answer

Explanation:

The discriminant, (#Delta#), is derived from quadratic equation:
#x=(b^2+-(sqrt(b^2-4ac)))/(2a)#

Where #Delta# is the expression beneath the root sign, hence:
The discriminant (#Delta#) =#b^2-4ac#

If #Delta#>0 there are 2 real solutions (roots)
If #Delta=0# there is 1 repeated solution (root)
If 0>#Delta# then the equations has no real solutions (roots)

In this case #b=-1#, #c=-6# and #a=2#
#b^2-4ac=(-1)^2-4(2)(-6)=49#

So your equation has two real solutions as #Delta#>0. Using the quadratic formula these turn out to be:

#x=(1+-(sqrt49))/(4)#

#x_1=2#

#x_2=(-6/4)=-1.5#