## College Algebra (11th Edition)

$\bf{\text{Solution Outline:}}$ To evaluate the discriminant of the given equation, $8x^2-72=0 ,$ identify first the value of $a,b,$ and $c$ in the quadratic expression $ax^2+bx+c.$ Then use the Discriminant Formula. If the value of the discriminant is less than zero, then there are $\text{ 2 nonreal complex solutions .}$ If the value is $0,$ then there is $\text{ 1 distinct rational solution .}$ If the value of the discriminant is a positive perfect square, then there are $\text{ 2 rational solutions .}$ Finally, if the value of the discriminant is positive but not a perfect square, there are $\text{ 2 irrational solutions .}$ $\bf{\text{Solution Details:}}$ In the equation above, $a= 8 ,$ $b= 0 ,$ and $c= -72 .$ Using the Discriminant Formula which is given by $b^2-4ac,$ the value of the discriminant is \begin{array}{l}\require{cancel} (0)^2-4(8)(-72) \\\\= 2304 \\\\= 48^2 .\end{array} Since the discriminant is $\text{ a positive perfect square ,}$ then there are $\text{ 2 rational solutions .}$