ADVANCE BUSINESS MATH’S

PRESENTED TO SIR RIZWAN YAZDANI

PRESENTED BY:MEHWISH ALI AKBER

ALMAS AMIR ALIMARINA KHAN

ALINA SHAH

TOPIC

QUADRATIC EQUATION

QUADRATIC EQUATION

A Quadratic Equation in Standard Form(a, b, and c can have any value, except that a

can't be 0.)

The letters a, b and c are coefficients (you know those values) The letter "x" is the variable or

unknown (you don't know it yet)

EXAMPLE

•The name Quadratic comes from "quad" meaning square, because of x2 (in other words x squared).

•It can also be called an equation of degree 2

SOME MORE EXAMPLES

In this one a=2, b=5 and c=3

EXAMPLES CONTINUED

This one is a little more tricky: Where is a? In fact a=1, because we don't usually write "1x2" b=-3 And where is c? Well, c=0, so is not shown.

EXAMPLES CONTINUED

Oops! This one is not a quadratic equation, because it is missing x2 (in other words a=0, and that means it can't be quadratic)

QUADRATIC FORMULA

If b²–4ac>0 there will be two real roots. If b²–4ac=0 there will be one real roots. If b²–4ac<0 there will be no real roots.

QUADRATIC FORMULA CONT.. Discriminant: The part (b2 - 4ac) is called the discriminant,

because it can "discriminate" between the possible types of answer:

when b2 - 4ac is positive, you will get two solutions when it is zero you get just ONE solution, and when it is negative you get two Complex solutions

SOLVING EXAMPLE: 5x² + 6x + 1 = 0

Example: Solve 5x² + 6x + 1 = 0

Coefficients are:   a = 5, b = 6, c = 1      

Quadratic Formula:   x = [ -b ± √(b2-4ac) ] / 2a    

Substitute a,b,c:  x = [ -6 ± √(62-4×5×1) ] / (2×5)      

Solve:

  x = [ -6 ± √(36-20) ]/10    

x = [ -6 ± √(16) ]/10  

  x = ( -6 ± 4 )/10    

x = -0.2 and -1

THANK YOU