How do you find the discriminant for #2x^2=5/2x+3/2# and determine the number and type of solutions?

1 Answer
Feb 13, 2017

Answer:

The Discriminant is 18.25 andthe equation has 2 distinct real roots

Explanation:

Using the quadratic formula #(-b +- sqrt(b^2 - 4ac))/(2a)#

The discriminant is calculated by using #b^2-4ac#

This allows discrimination between the different types of roots for a quadratic
#>0# the equation has two roots
#=0# the equation has a single root
#<0# the equation has imaginary roots.

Rearranging the quadratic given
#2x^2 -5/2x -3/2 = 0#

Substituting in the values from the quadratic into the formula above
#(5/2)^2 - 4*2*(-3/2)#

Simplifying
#6.25 + 12#

The discriminant is 18.25 and the quadratic has two distinct real roots because the value is greater than 0