quadratic formula
The roots of the quadratic equation
are given by the formula
The number is called the discriminant of the equation.If , there are two different real roots,if there is a single real root,and if there are no real roots (but two different complex roots
).
Let’s work a few examples.
First, consider .Here , , and .Substituting in the formula gives us
So we have two solutions (depending on whether we take the sign or ): and .
Now we will solve .Here , , and , so
and the solutions are and .
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 |