How do you find the discriminant and how many and what type of solutions does #2x^2 - 3x + 4 = 0# have?

1 Answer
May 17, 2015

#2x^2-3x+4# is of the form #ax^2+bx+c#, with #a=2#, #b=-3# and #c=4#.

The discriminant can be calculated using the formula as follows:

#Delta = b^2-4ac = (-3)^2-(4xx2xx4) = 9-32 = -23#

This is negative, so #2x^2-3x+4 = 0# has two distinct complex roots and no real roots.

The possible cases are:

#Delta > 0# : Two distinct real roots.
#Delta = 0# : One repeated real root.
#Delta < 0# : No real roots (two distinct complex ones).