quadratic formula

The roots of the quadratic equation

ax2+bx+c=0  a,b,c,a0

are given by the formula


The number Δ=b2-4ac is called the discriminantPlanetmathPlanetmathPlanetmath 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 rootsMathworldPlanetmath).

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


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


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