November 15,2010

Hey guys Its Deep

In our Maths class , We learnt about the sum and product of roots . In this last weekend Mr. Piatek told us to collect the information about the imaginary numbers . Few students pasted the information about imaginary numbers in briefly and very nicely . Mr.P gave them bonus points Here is the information about the sum and product of roots.

the quadratic formula

x=2a−bb2−4ac

give the roots of a quadratic equation which may be real or imaginary. The sign in the radical indicates that

x1=2a−b+b2−4ac and x2=2a−b−b2−4ac

where x1 and x2 are the roots of the quadratic equation ax2+bx+c=0. The sum of rootsx1+x2 and the product of roots x1x2 are common to problems involving quadratic equation.

Derivation of the Sum of Roots

x1+x2=2a−b+b2−4ac+2a−b−b2−4ac
x1+x2=2a−b+b2−4ac−b−b2−4ac

x1+x2=2a−2b

answer is -b/a

Derivation of the Product of Roots

x1x2=2a−b+b2−4ac2a−b−b2−4ac

by taking this formula we get

the formula is c/a

Example

What are the sum and product of the roots of

4x² -3x + 2

here the value of b= -3, a=4

Solution

The sum is

b 3
- =
a 4

and the product of the roots is

c 2 1
= =

Equation	Values of 'a', 'b' and 'c'	One Root (x)	Other Root (x)	Sum of Roots (x + x)	Product of Roots (xx)
	a = 3, b = 10, c = 7	x = -1		(-1)+ +=	(-1)=7/3

that are the some of examples related to sum of roots and product of roots we did in class.

see u tomorrow

important notice:-the assignment of algebra is due on November 25,2010

The mental math quiz is on wednesday

see u tomorrow

byeeeeeeeeeeee