quadratic equation

In this project I will introduce you to:

-definition

-exampes

-an easier way to remember formula

-and more rules about quadratic equation

Definition:

In mathematics, the second degree polynominal equation is called quadratic equation.

ax^2+bx+c=0 - general form of quadratic equation with one variable

The value of the variable x, for which the equation ax2+bx+c=0, a is diffrent of 0, transfers in numerical equation is the solution or the root of the equation.

a,b,c- are known, a can not be 0

x- is the variable or unknown

The quadratic equation can be:

• full
• incomplete

FULL QUADRATIC EQUATION:

Ex.

(x-2)(2x-3)=6 x1/2=-b+_D\2a

2x2-3x-4x+6=6 x1= -7+7\4

2x2-7x=6-6 x1=0\4

2x2-7x=0 x1=0

a=2;b=-7;c=0 x2=-7-7\4

D=b2-4ac x2=-14\4

D=(-7)2-4*2*0 x2=-7\2

D=49

D- discriminant

IF:

D>0 - real solutions

D=0 -two equal real solutions

D<0 - conjucted-complex solutions

INCOMPLETE QUADRATIC EQUATION

Ex.

x(x-3)+2x(2-x)=x-16

x^2-3x+4x-2x^2=x-16

x^2-3x+4x-2x^2-x+16=0

-x^2-4x+4x+16=0

-x^2+16=0

-x^2=-16/(-1) x1=4

x^2=16 x2=-4

This is an easier way to remember this formula:

"x is equal to minus b

plus or minus the square root

of b-squared minus 4 ac

ALL over 2 a"

"All around the milberry bush

the monkey chased the weasel

the monkey thought it was all in fun

Pop! goes the weasel"