Science Term: quadratic equation

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quadratic equation

Definition/Summary

A second order polynomial equation in one variable, its general form is [itex]ax^2 + bx + c = 0,[/itex] where x is the variable and a, b, and c are constants, and [itex]a \ne 0.[/itex]

Equations

[tex]ax^2 + bx + c = 0[/tex]

Scientists

Recent forum threads on quadratic equation

Breakdown

Mathematics
> Algebra
>> Equations

Images

Extended explanation

Since a quadratic equation is a second degree polynomial equation, then the fundamental theorem of algebra states that two complex roots exist, counting multiplicity.

There are various analytical methods used for finding the roots of quadratic equations, one of the most common methods is the so-called quadratic formula and is derived by completing the square on the general expression shown above. The quadratic formula may be written thus,

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\hspace{2cm}a\neq0[/tex]

The term under the square root is known as the discriminant and can be used to determine the form of the roots of the quadratic equation.

If [itex]b^2-4ac > 0[/itex] then there are two distinct real roots. Furthermore if the discriminant is a perfect square, then the two roots are also rational.

If [itex]b^2-4ac = 0[/itex] then there is one repeated real root.

If [itex]b^2-4ac < 0[/itex] then there are two distinct non-real roots. These two roots are the complex conjugate of each other.

Commentary

Hootenanny @ 06:12 AM Nov30-09

SREEDHARACHARYA'S RULE is better known as "completing the square". Perhaps it would be instructive to include a derivation of the quadratic formula using completing the square. I'll add a derivation if I have time this weekend.

obing @ 10:49 AM Nov14-09

@ tiny-tim SREEDHARACHARYA'S RULE is about finding the root of the equation like
x = -b ± √(b"-4ac) / 2a and solving for x

obing @ 10:38 AM Nov14-09

graphical influence of physical quantity involving 2 degree variables would be of much help. it would help understanding 2 dimension more clearly

mhaze @ 10:41 PM Sep12-09

I prefer you to explain in polynomials form. arigatou

coolmadhwa @ 09:45 AM Feb27-09

it would have been better if u would have explained quadratic equations using graphs

matqkks @ 03:11 PM Nov20-08

The reason for the name discriminate for b^2-4ac is that it disciminates between real and complex roots.

olgranpappy @ 09:01 PM Oct29-08

... and I don't find any mention of that particular name here:

http://en.wikipedia.org/wiki/Quadratic_equation#History

olgranpappy @ 08:57 PM Oct29-08

"SREEDHARACHARYA'S RULE" (a.k.a. "Sridharacharya's formula") is known in the west as "the quadratic formula".

I'm sure the quadratic formula has many other names in many other places too...

Caren vUwB @ 05:51 AM Aug19-08

I only know 3 methods to find roots of quadratic equation
1. Factorization
2. Formula
3. Completing Square
I most hated completing square because it always make me confused.

tiny-tim @ 06:03 AM Jul22-08

What is SREEDHARACHARYA'S RULE? I googled and wiki'd it, but couldn't find it.

@ 06:53 AM Jun2-08

This entry should also explain SREEDHARACHARYA'S RULE.
-Sourojit Das.

@ 08:05 AM May24-08

Ax^2 + Bx + C = o

Ax^2 + Bx = -C

(4A)(Ax^2 + Bx) = -4AC

4A^2x^2 + 4ABx + B^2 = -4AC + B^2

(2Ax + B)^2 = -4AC + B^2

2Ax + B = Sqrt( B^2 - 4AC)

x = -B Sqrt(B^2 - 4AC) / 2A

Defennder @ 09:37 AM May18-08

Why doesn't this entry cover quadratic expressions in terms of both x and y ? It has only done so for x.

@ 07:56 AM May16-08

i agree with the first comment at least the derivation of the formula and their relation to their coefficients as well as the sub-topics and examples

angyansheng @ 05:12 AM May14-08

The article should include the derivation of the quadratic formula to make it more complete i.e. the "completing the square" technique.
See new entry complete the square - tiny-tim

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