The equation ax^2 + 190 x + c has a given factor of px +q. What is the product of ac?

This isn’t a real SAT question for a few reasons. First, it calls an *equation*, but an equation requires two sides and an equals sign—this is just an expression. Second, and about equally as important, I haven’t seen any real SAT questions that test whether you know how to work with the discriminant like this. A useful concept in real math but only marginally useful (if at all) for the SAT. Third, and most important, there’s not just one answer here, unless you make assumptions about the question is really asking. This is something you find all the time in fake questions; on a real question you never need to wonder what they’re actually asking.

So anyway.

The discriminant of a quadratic expression is , which you will probably recognize as the part under the square root sign in the quadratic formula. If the discriminant is positive, then there are two real roots. If the discriminant is negative, there are two complex roots. If the discriminant is exactly zero, then there is exactly one root (i.e., the quadratic is a perfect binomial square).

I’m going out on a limb and assuming that when the question says that we have “*a* given factor” it really means “*only one* factor,” which would mean that we can assume is a perfect square, and therefore that its discriminant equals zero.

Otherwise, we’d have to assume that is one of two real roots, in which case we’d be solving an inequality instead of an equation: