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

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