quadratic formula
The number Δ=b2-4ac is called the discriminant of the equation.
If Δ>0, there are two different real roots,
if Δ=0 there is a single real root,
and if Δ<0 there are no real roots (but two different complex roots
).
Let’s work a few examples.
First, consider 2x2-14x+24=0. Here a=2, b=-14, and c=24. Substituting in the formula gives us
x=14±√(-14)2-4⋅2⋅242⋅2=14±√44=14±24=7±12. |
So we have two solutions (depending on whether we take the sign + or -): x=82=4 and x=62=3.
Now we will solve x2-x-1=0. Here a=1, b=-1, and c=-1, so
x=1±√(-1)2-4(1)(-1)2=1±√52, |
and the solutions are x=1+√52 and x=1-√52.
Title | quadratic formula |
Canonical name | QuadraticFormula |
Date of creation | 2013-03-22 11:46:15 |
Last modified on | 2013-03-22 11:46:15 |
Owner | yark (2760) |
Last modified by | yark (2760) |
Numerical id | 13 |
Author | yark (2760) |
Entry type | Theorem |
Classification | msc 12D10 |
Classification | msc 26A99 |
Classification | msc 26A24 |
Classification | msc 26A09 |
Classification | msc 26A06 |
Classification | msc 26-01 |
Classification | msc 11-00 |
Related topic | DerivationOfQuadraticFormula |
Related topic | QuadraticInequality |
Related topic | QuadraticEquationInMathbbC |
Related topic | ConjugatedRootsOfEquation2 |
Related topic | QuadraticCongruence |