How to use the discriminant to find out what type of solutions the equation has for #3x^2 - x + 2 = 0#?

1 Answer
Mar 26, 2018

Answer:

Zero roots

Explanation:

Quadratic formula is #x=(-b+-sqrt(b^2-4ac))/(2a)#
or
#x=-b/(2a)+-(sqrt(b^2-4ac))/(2a)#

We can see that the only part that matters is #+-(sqrt(b^2-4ac))/(2a)#
as if this is zero then it says that only the vertex #-b/(2a)# lies on the x-axis

We also know that #sqrt(-1)# is undefined as it doesn't exist so when #b^2-4ac=-ve# then the function is undefined at that point showing no roots

Whilst if #+-(sqrt(b^2-4ac))/(2a)# does exist then we know it is being plussed and minused from the vertex showing their are two roots

Summary:
#b^2-4ac=-ve# then no real roots
#b^2-4ac=0# one real root
#b^2-4ac=+ve# two real roots

So
#(-1)^2-4*3*2=1-24=-23# so it has zero roots