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单词 QuadraticFormula
释义

quadratic formula


The roots of the quadratic equation

ax2+bx+c=0  a,b,c,a0

are given by the formula

x=-b±b2-4ac2a.

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

x=14±(-14)2-422422=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.

Titlequadratic formula
Canonical nameQuadraticFormula
Date of creation2013-03-22 11:46:15
Last modified on2013-03-22 11:46:15
Owneryark (2760)
Last modified byyark (2760)
Numerical id13
Authoryark (2760)
Entry typeTheorem
Classificationmsc 12D10
Classificationmsc 26A99
Classificationmsc 26A24
Classificationmsc 26A09
Classificationmsc 26A06
Classificationmsc 26-01
Classificationmsc 11-00
Related topicDerivationOfQuadraticFormula
Related topicQuadraticInequality
Related topicQuadraticEquationInMathbbC
Related topicConjugatedRootsOfEquation2
Related topicQuadraticCongruence
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更新时间:2025/5/4 6:45:25