quadratic function

hi this is john.. I'm the scribe of the day.. we started our lesson by discussing writing a quadratic equation when roots is given..

WRITING A QUADRATIC EQUATION WHEN ROOTS IS GIVEN

If the roots of the equation are known, the equation can be found,it is...
x²+ (-sum of roots)x + (product of roots) = 0
Finding the sum of roots using Quadratic Formula = -b + Ö b²-4ac + -b - Ö b²-4ac2a 2a
= -b + Ö b -4ac -b-Ö b-4ac2a
= -2b = -b2a a
SUM OF ROOTS = R1 + R2 = -b/a

Finding the product of roots = (-b +Ö b²-4ac / 2a) (-b-Ö b²-4ac / 2a)
=b² - b Ö b²-4ac + b Ö b²-4ac - (b²-4ac)4a²
= b ²- (b²-4ac)4a²= 4ac / 4a²= c /a

PRODUCT OF ROOTS = R1*R2 = c /a

It came from the formula of the quadratic equation
x² + (-sum of roots) x + (product of roots) = 0
x² + -b/a x + c/a = 0

Example: Given the roots(-2,4) state the quadratic equation

1)Find the sum of the roots = -b/aSum=r1+r2 =-2+4=2 -b/a=2 so b/a=-2

2)Find the product=r1*r2 = (-2)(4)= -8 -8=c/a

3)Plug in x² + (-b/a) x + c/a=0x²+(-2)x +-8 =0
x² -2x - 8=0

Ex: Given the two roots (-6,-1) state the quadratic equation

Sum of roots -6 + -1= -7-b/a=-7 so b/a=7

Find the product =r1*r2 = (-6 -1)=6 so c/a=6x² + -b/a x + c/a=0

check:(x+6)(x+1)=0
roots x=-6x=-1

Ex.)GIVEN THE ROOTS:(7+ Ö 13 , -7 Ö 13) state the quadratic equation

SUM= 7+ Ö 13 + 7- Ö 13 =14/3 =-b/a so b/a=-14/33 3

Product =(7+ Ö 13) (7- Ö 13) = 49 -7 Ö 13+ 7 Ö 13 -13 = 36/9 = 4
3 3 9
so c/a = 4

the equation x² + -b/a x + c/a =0 x² -14/3 x + 4=0

becomesQuadratic Equation = 3x² -14x +12 =0

REMEMBER: When Given the two roots of a quadratic,the equation is [x² + -b/a x + c/a =0]where -b/a =the sum of the roots and c/a =the product of the roots.

The next scribe is luis.

Classmates if u have question..dont be shy to ask for my help because im having a hard time doing this blog. thanks.