Can someone help me understand how to get to -4? When solving for the roots, it does not result in whole numbers. When I apply the quadratic formula, it results in a rather time consuming and difficult product of (-5 +/- root (41)) / 2).

Is there a simpler way to solve it that I am missing?

Thank you in advance for the help!

The product of the roots will be of the form:

(a+b) * (a-b) = a² - b², where a = -5/2 and b = √41/2

This gives (25/4) - (41/4) = -16/4 = -4

Additionally, if you want to remember a shortcut, if we are given an equation of the form ax^{2} + bx + c = 0,

- The sum of roots = -b/a
- The product of roots = c/a

Here, a=1, c = -4 and c/a gives -4

The roots would be

\frac{-5 + \sqrt{41}}{2}

and

\frac{-5 - \sqrt{41}}{2}

Finding the product isn’t all that hard manually:

\frac{-5 + \sqrt{41}}{2} \times \frac{-5 - \sqrt{41}}{2}

=\frac{1}{4} (-5 + \sqrt{41})(-5 - \sqrt{41})

=\frac{1}{4}(41 - 25)

=4

Note that knowledge of Vieta’s formulas (as @vision_35 said with his shortcuts) is not required for the GRE.