QUADRATIC EQUATION (LECTURE 1)

LESSON 1 QUADRATIC EQUATION.

GOOD MORNING!!

Today's learning outcomes:
I WILL BE ABLE TO;
1. recall general form of a quadratic equation
2. identify  any  given equation as quadratic .
3.to form quadratic equations from word problems . 
                               

What is Quadratic Polynomial

P(x) = ax2 +bx+c   where a≠0

It is a polynomial of degree 2

Examples:

$P\left(x\right)=3x^2-11x-2$
$P\left(x\right)=x^2-x-11$
$P\left(x\right)=x^2+x-897$

Then 

What is a Quadratic equation ?

 see the video

So  a Quadratic equation is

When we equate Quadratic Polynomial with zero, it is called Quadratic equation
 or

  A quadratic equation in the variable x is  an equation of the form 
$a{x}^2+bx+c=0$ where a.b,c  are real numbers and  a ≠0. 

Examples:

$6x^2-x-2=0$
$x^2-x-20=0$
$x^2+x-300=0$

So lets find out

Q 1 which of these is not a quadratic equation?

$\mathrm{(i)\; 2}{x}^2-6x+5=0$

$(ii)\; (x-2\left)\right(x+1)=(x-1\left)\right(x+3)$

$(iii)\; (2x-1\left)\right(x-3)=(x+5\left)\right(x-1)$

(iv)   None of these
Answer ---------------------------------

  











so have you got it correct  
yes (ii) is not a quadratic equation
(x−2)(x+1)=(x−1)(x+3) ...............(why ?)$(x-2)(x+1)=(x-1)(x+3)$


⇒x2−2x+ 1x - 2=x2−1x + 3x - 3  on solving the bracket $2x^2-6x+5=0$
⇒ -1x  - 2  =  2x - 3
⇒ 3x  = 1  ..............................( linear equation)

linear equation ⟶ degree     ------------
quadratic  equation   ⟶  degree --------

LETS SOLVE Q1 OF Ex 4.1 



 SOLUTION  1

 



WHERE  IS  QUADRATIC EQUATION USED ?

It is used in many field and it has many application in Mathematics

For example
John has a area of a rectangular plot is 528 m2.The length of the plot (in meters) is one more than twice its breadth. We need to find the length and breadth of the plot

For solution , we can assume breadth is x m ,                                                           then length  would be (2x+1) m
 Area of rectangular  plot = length x breadth                                                                 Now $528=x(2x+1)$
or $2x^2+x-528=0$
Which is a quadratic equation and the required representation of the problem mathematically

 THE QUESTION  YOU UNDERSTOOD IS Q2 (i) of Ex 4.1

  Q2 (iii) 

 solution 2 (iii)

  

LET'S SEE THE VIDEO

nOW YOU 

 As you understood the word problem  related to speed of train 

 Similarly Now you can solve Q2 (iv)  of Ex 4.1 for Homework

Ex 4.1 Q1  ( iii,iv,v,vi,vii)  Q2 ( ii)

AQAD

Q. The sum of ages of a son and his father is 36 years and the product of their ages is 180. The difference of father's and son's  age is

30

26

24
none of these

You must have solved Q2(iv) ,now  check  

17 SDG

TAKE CARE OF YOURSELF AND HAVE A NICE DAY