Question

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

Answer 1

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