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 $\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

The discriminant is calculated by using ${b}^{2} - 4 a c$

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
$2 {x}^{2} - \frac{5}{2} x - \frac{3}{2} = 0$

Substituting in the values from the quadratic into the formula above
${\left(\frac{5}{2}\right)}^{2} - 4 \cdot 2 \cdot \left(- \frac{3}{2}\right)$

Simplifying
$6.25 + 12$

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