QUADRATIC EQUATIONS ( LECTURE 6)

18TH MAY LESSON 6

GOOD MORNING 

TODAYS LEARNING OUTCOMES 
I will be able to solve word problems based on age and marks 

How to solve Quadratic word problems

Quadratic word problems

We have seen how to solve the quadratic equations ,now lets take a look at the real world problem and how we can apply the quadratic equation formula to solve them

Let start with an example
"In a class test, the sum of  shefali  marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects."

How to approach this Problem

a) First we need to carefully read the problem and understand the situation. Here we need to find marks.

 Let us marks in Maths as  x

Then as per problem

Marks in English would be = $30-x$

b) Now If she got 2 marks more,then Maths marks would = $\left(\mathrm{x+}2\right)$
c) If she got 3 marks less in english,then english marks would = $(30-x-3)=(27-x)$

d) As per problem, the product is equal to 210 so$(x+2)(27-x)=210$
$-x^2+25x+54=210$
or
$x^2-25x+156=0$

So this is quadratic equation , we can solve by any methods, Solving by factorising 

or x =12 or 13

So Shefali maths marks is 12, the english marks are 18
and  Shefali  maths marks is 13, the english marks are 17
Similary we can solve the other quadratic word problems

 T he video  can help you to understand 

Lets see one more example 

Question

If zeba were younger by 5 years than what she really is then the square of her age would have been 11 more than five times her actually age. What is her age now?

solution 

let Zeba's present age be     ____  yrs

  

  5 years ago

 Zeba's age  was =      (  x  -  ___  ) yrs 

As per the question

 (x−5)2=______________

x2+25−10x=11+5x          ( Identity    (a−b)2     = a 2 - 2ab+  b2) 

x2− ______   +14=0

 x2−14x−x+14=0     ( NOTE :  It can be solved by  Factorisation  or  Quadratic  Formula ) 

(x-1)(x-14) =0                  By  Factorising 

 x = 1  and x = 14

  if x = 1, then Zeba's present age will be   1 year old and her age 5 years ago would be  then 1 - 5  = - 4   

   

 therefore  x =1 is rejected 
So Zeba's  age is  14 yrs 


Example
The sum of the ages of two friends A and B is 20 years. Four years ago, the product of their ages in years was 32 .
Solution

Here we need to advise if that is a possible condition

Let the age of A be x years.

then the age of the B will be (20 - x) years.

Now 4 years ago,

Age of A = (x - 4) years

Age of N = (20 - x - 4) = (16 - x) years
So we get that,
$(x-4)(16-x)=32$
$16x-x^2-64+4x=32$
$x^2-20x+\mathrm{96=}0$

$\mathrm{<br>}$

Home work  
 Find the age of both the friends 
  

solve Q4 of execise 4.3 and Practice the questions 

Quiz Time

Question 1 What is the Solution of Quadratic equation
$x^2+16=0$
 A) 4,-4
 B) No real roots
 C) 4
 D) -4
Question 2 What is the solution of Quadratic equation
$2x^2-32=0$
 A) 4,0
 B) -4,0
 C) 4,-4
 D) No real roots
Question 3 What is the solution of Quadratic equation
$6x^2-7x+2=0$
 A) 2/3,1/2
 B) 1/3,1/2
 C) -1/2,1/3
 D) -2/3,1/2
Question 4 which of following statement is True
 A) Every quadratic equation has at least two roots
 B) Every quadratic equations has at most two roots.
 C) Every quadratic equation has exactly one root
 D) none of these
Question 5 Which of the following equations has 2 as a root?
 A) $y^2-4y+5=0$
 B) $y^2+3y-12=0$
 C)$3y^2-6y-2=0$
 D) $2y^2-7y+6=0$
Question 6 Is .3 root of quadratic equation?
$x^2-.9=0$
 A) True
 B) False

 I WOULD ENCOURAGE THE STUDENTS TO SOLVE AND THEN CHECK THE 
ANSWER

Question 4:

The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is. Find his present age.

ANSWER:

Let the present age of Rehman be x years.

Three years ago, his age was (x − 3) years.

Five years hence, his age will be (x + 5) years.

It is given that the sum of the reciprocals of Rehman’s ages 3 years ago and 5 years from now is.

However, age cannot be negative.

Therefore, Rehman’s present age is 7 years

QUIZ     Answers  :-  B,C,A,B,D,B

THANK YOU AND HAVE A NICE DAY