Quadratic equations are a key component of GMAT Quant, testing not just your algebra skills but your logical reasoning. This guided path will teach you the core solving methods, crucial shortcuts, and the specific strategies needed for Data Sufficiency.
Start with the core definition of the quadratic equation and use our interactive verifier to understand what the "roots" of an equation represent.
A Quadratic Equation has the form $$ ax^2 + bx + c = 0 $$
The Roots are the specific values of 'x' that make the equation true (equal to zero). Every quadratic has exactly two roots.
Learn the step-by-step process of factoring quadratic expressions to find the roots. This is a crucial skill for speed and efficiency.
Goal: Rewrite $$ ax^2 + bx + c = 0 $$ into $$ (x+m)(x+n) = 0 $$.
Shortcut (when a=1): Find two numbers that multiply to 'c' and add to 'b'.
Master the universal tool for solving any quadratic equation. Our interactive calculator shows you how to apply the formula step by step.
The universal method for any quadratic:
The term inside the root, $$ b^2 - 4ac $$, is called the Discriminant.
Learn how the discriminant (b²-4ac) tells you the "nature" of the roots (2, 1, or 0 real roots) without solving the equation—a vital DS concept.
The expression $$ b^2 - 4ac $$ is called the Discriminant. It tells us the nature of the roots without solving.
$$ a=1, b=-8, c=15 $$
$$ D = (-8)^2 - 4(1)(15) = 64 - 60 = 4 $$
Discriminant is Positive.
Result: Two distinct real roots. (Because we add/subtract a real number).
Learn the formulas for finding the sum (-b/a) and product (c/a) of the roots *without* solving, a critical time-saver for advanced questions.
For $$ ax^2 + bx + c = 0 $$, you can find the sum and product of roots directly from coefficients.
$$ \text{Sum} = -b/a $$ | $$ \text{Product} = c/a $$
For the equation $$ 2x^2 - 10x + 12 = 0 $$
What is the SUM of the roots?
Practice the skill of building a quadratic equation from a given set of roots, a common way this concept is tested.
Enter the two roots to build the original Quadratic Equation.
Learn the complete method for solving quadratic inequalities by finding critical points and testing regions on a number line.
Solve for x: $$ x^2 - 2x - 8 < 0 $$
Solve $$ x^2 - 2x - 8 = 0 $$
$$ (x-4)(x+2) = 0 $$
Roots: x = 4, x = -2
Test a point between -2 and 4 (e.g. 0).
$$ 0^2 - 2(0) - 8 = -8 $$
-8 < 0 is TRUE.
The parabola dips below the axis between the roots.
$$ -2 < x < 4 $$
Put your understanding of GMAT Quadratic Equations: A Guide to Advanced Algebra & Logic to the test with our premium, adaptive practice questions. Build pacing efficiency and eliminate knowledge gaps now.
Stop calculating! Learn how to use the properties of symmetry to solve hard SD questions in seconds.
How to use 'Extreme Values' to find the range of a sum without calculating every fraction.
Learn how to use the 'Variance Test' to solve hard GMAT CR questions. We break down a classic 700-level Supply vs. Demand fallacy.