Difference between revisions of "Quadratic formula"

Revision as of 01:07, 19 June 2006

The quadratic formula is a general expression for the solutions to a quadratic equation.

Let the quadratic be in the form $a\cdot x^2+b\cdot x+c=0$ .

Moving c to the other side, we obtain

$ax^2+bx=-c$

Dividing by ${a}$ and adding $\frac{b^2}{4a^2}$ to both sides yields

$x^2+\frac{b}{a}x+\frac{b^2}{4a^2}=-\frac{c}{a}+\frac{b^2}{4a^2}$ .

Factoring the LHS gives

$\left(x+\frac{b}{2a}\right)^2=\frac{b^2-4ac}{4a^2}$

As described above, an equation in this form can be solved, yielding

${x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}}$

This formula is also called the Quadratic Formula.

Given the values ${a},{b},{c}$ , we can find all real and nonreal solutions to the quadratic equation.

Revision as of 21:00, 17 June 2006 (view source) Chess64 (talk \| contribs) (→‎General Solution For A Quadratic by Completing the Square) ← Older edit		Revision as of 01:07, 19 June 2006 (view source) MCrawford (talk \| contribs) (added definition (first sentence)) Newer edit →
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		+	The '''quadratic formula''' is a general expression for the [[solutions]] to a [[quadratic equation]].
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	===General Solution For A Quadratic by Completing the Square===		===General Solution For A Quadratic by Completing the Square===