The Number Under the Root
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 49 of 63.
The expression under the formula's root, b^2 - 4ac, has its own name: the discriminant. It is the first thing to compute, and everything after depends on it.
For x^2 + 5x + 6 = 0 the discriminant is 5^2 - 4 * 1 * 6 = 25 - 24 = 1. A perfect square under the root, like this 1, means the root is whole and the answers are tidy fractions or integers.
Compute it carefully: square b first, then subtract the product 4ac, signs and all. Most formula errors are discriminant errors, and they happen in this one line, which is why it deserves a lesson of its own.
Challenge
MediumThe equation x^2 + 5x + 4 = 0 has discriminant 5^2 - 4 * 1 * 4. Work it down by hand: type each line until one number remains.
Try it yourself
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Factoring & Quadratics
1What Factoring Is
Two DirectionsThe Reverse GearUn-Distributing LettersThe Check Is MultiplicationRecap: First Factors4Minus Signs in the Machine
A Negative ProductWhich One Gets the MinusBoth NegativeThe Sign MapRecap: Signs7The Zero Product Rule
A Product That Makes ZeroOne Factor Is EnoughThe Bare XEvery Factor Gets a TurnRecap: Zero Product10The Quadratic Formula
The Formula, StatedThe Number Under the RootSplit the Plus-MinusIt Always WorksChoosing a MethodRecap: The Formula2The Greatest Common Factor
Number and Letter TogetherThe Largest OneHigher PowersThree Terms Share TooRecap: The GCF5Special Shapes
A Missing MiddleThe Shape in LettersThe Perfect SquareThe Minus VersionPrime PolynomialsRecap: Special Shapes3The Sum-Product Machine
Reading the ProductHunting the PairThe Machine in LettersLonger HuntsRecap: The Machine6Factor Completely
Two LayersSquares InsideCompletely Means CompletelyThe Deep CheckRecap: Factor Completely