GRE-Style: Quadratic with Unknown Coefficients

GRE Quantitative · Axiom Academy

EXAMPLE GRE-Style: Quadratic with Unknown Coefficient k Use a known root to pin down an unknown coefficient, then compare quantities. The equation x^2 - kx + 12 = 0 has x = 3 as one of its solutions, where k is a constant. Nice work — you pinned down an unknown coefficient from a known root, then used it to compare two quantities. Plug in what you know: a known root always satisfies the equation — substitute it in and solve for the unknown coefficient directly. Vieta's shortcut: once you know one root and the constant term, the product of the roots (here, 12 ) hands you the other root instantly — no factoring or quadratic formula needed. Compare, don't over-solve: in Quantitative Comparison, you only need enough algebra to decide A vs B vs equal vs "can't be determined" — you don't need every detail of the full solution. Result: k = 7 , so Quantity B ( 8 ) is greater. This same move — substitute a known value, solve for the unknown coefficient, then reason about the rest — works whether you're comparing two expressions, evaluating a function at two inputs, or checking a quadratic's roots.

This is the written version of the interactive lesson above. See the full GRE Quantitative course.