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...he brackets and moving the number 125 to the left-hand side gives us the [[quadratic equation]] ...ta=(-4)^2-4\cdot 125=-484=-22^2</math>, which is ''negative'', so that the quadratic equation has ''no real solution'': the usual formulae giving the solutions require t

...is <math>b^2 - 4ac</math>, which plays a key part in the solution of the [[quadratic equation]].

{{r|Quadratic equation}}

{{r|Quadratic equation}}

{{r|Quadratic equation}}

...ives a geometric construction with Euclidean tools for the solution of the quadratic equation for positive real roots. The construction is due to the Pythagorean School ...quations]] with up to five unknowns, the general algebraic formula for the quadratic equation, and solutions of indeterminate quadratic equations and simultaneous equati

{{r|Quadratic equation}}

In characteristic zero, every [[quadratic equation]] is soluble by taking one square root, so a quadratic field is of the form

{{r|Quadratic equation}}

...cas sequences have one common characteristic: they can be generated over [[quadratic equation|quadratic equations]] of the form: <math>\scriptstyle x^2-Px+Q=0\ </math> w of the quadratic equation <math>\scriptstyle x^2-Px+Q=0</math>.

...e blank between the brackets. Completing the square is used for solving [[quadratic equation]]s (the proof of the well-known formula for the general solution consists o

The polar equation is a quadratic equation in ''r''². It has real roots if the [[discriminant]] ''D'' is po

Multiplying both sides by [AB] and rearranging gives a quadratic equation:

which provides a quadratic equation to determine an appropriate value for ''C_C''.

...es of algebraic numbers have been studied for millennia as solutions of [[quadratic equation]]s. They appear indirectly in the [[cakravāla]] method from the 11th cent

Switching back to a quadratic equation Clearly, in order to determine ''a priori'' whether the quadratic equation represents an ellipse,

Switching back to a quadratic equation Clearly, in order to determine ''a priori'' whether the quadratic equation represents an ellipse,

a [[quadratic equation]] with the solutions

...operations for the systematic solution of [[linear equation|linear]] and [[quadratic equation]]s. ...class of problems typically solved today by using [[linear equation]]s, [[quadratic equation]]s, and [[indeterminate equation|indeterminate linear equation]]s. By contr

...of the brackets and move the number 125 to the left-hand side to get the [[quadratic equation]] ...ta=(-4)^2-4\cdot 125=-484=-22^2</math>, which is ''negative'', so that the quadratic equation has ''no real solution'': the usual formulae giving the solutions require t