IT'S A PRESENTATION ON QUADRATIC EQUATION PART 1, CLASS 10, CHAPTER 4, IT STARTS WITH THE SHAPE PARABOLA AND IT'S DAY TO DAY LIFE EXAMPLES, AS WE PROCEED FURTHER WE SOLVE SOME EXPRESSIONS, WE COVERT IT INTO QUADRATIC EQUATIONS. AFTERWARDS, WE LEARN HOW TO FORM STANDARD QUADRATIC EQUATIONS WITH EXAMPLES (WORD PROBLEMS).
11. After simplification:-
S.NO. EXPRESSIONS
1 3(x2+7)
2 (x+4)(x+4)
3 2x(x-4)
4 (x+7)(x+3)
SOLUTIONS
3x2 + 21
x2 + 8x +16
2x2 – 8x
x2 + 10x + 21
Q1.Are these expressions are polynomials?
Ans.YES
Q2.What common characteristics do these polynomials have?
Ans.Degree of these polynomials : 2
12. Second degree polynomials are known as quadratic polynomial
When a quadratic polynomial is equated to something , it is known as a
quadratic equation.
Example : x2 + 5x … (Quadratic polynomial)
x2 + 5x = 50 ... (Quadratic equation)
13.
14. The name Quadratic comes from "quad" meaning square.
A quadratic equation is any equation having the standard form :
where,
x is a variable or unknown(we don’t know yet)
a, b and c are real numbers and a ≠ 0.
The real numbers a,b,and c are the coefficients of the equation
It is also called an "Equation of Degree2”
Note : If a = 0,then the equation is linear, not quadratic.
DEFINITION :-
ax2 + bx + c = 0
15. Check whether the equation is quadratic equations : (x + 1)2 = 2(x – 3)
Solution :-
(x + 1)2 = 2(x – 3)
(x)2 + 12 + 2*(x)(1) = 2*(x) – 2*3
x2 + 1 + 2x = 2x – 6
x2 + 1 + 2x – 2x + 6 =0
x2 + 1 + 0 + 6 =0
x2 + 7 = 0
Comparing it with standard form : ax2 + bx + c = 0
We get , a = 1 , b = 0 , c = 7
Since , a ≠ 0 and highest degree of x is = 2
Therefore , it is a QUADRATIC EQUATION.
Example 1
16. S.NO. Equations Standard Form a b c
Is it a
Quadratic
equation ?
1 12x2 +16 = - 8x 12x2 + 8x +16= 0 12 8 16 Yes
2 3x + 21 = 0 0x2 + 3x + 21 =0 0 3 21 No
3 x2 + 21= 10x x2 -10x + 21= 0 1 -10 21 Yes
Complete the table
17. Represent the given following situations in the form of quadratic equation.
a) Suppose a charity trust decides to build a prayer hall having
a carpet area of 300 square meters with its length
one meter more than twice its breadth.
Solution:
Let the breadth of the prayer hall be x meters
Therefore, length of the prayer hall = (2x +1) meters
Now, area of hall = (2x+1)*(x) m2
= (2x2 + x ) m2
So , 2x2 + x = 300 (Given)
300 sq. m
(2x+1) meters
xmeters
2x2 + x – 300 = 0
Example 2
18. b ) Rohan’s mother is 26 years older than him. The
product of their ages (in years) 3 years from now will
be 360. Represent the situation in the form of
quadratic equation.
Solution:
Let the present age of Rohan be x years
Therefore, Mother’s present age = (x + 26) years
According to question ,
x years
x + 26 years
19. After 3 years
Rohan’s age = (x + 3) years
Mother’s age = (x+ 26 +3) years = (x +29) years
The product of their ages (in years) 3 years from
now will be 360
So, ( x + 3)(x+29) = 360 (Given)
x*( x+29) + 3*( x+29) = 360
x2 + 29x +3x +87 = 360
x2 + 32x + 87 = 360
x2 + 32x + 87 – 360 = 0
x2 + 32x – 273 = 0
x2 + 32x – 273 = 0
x + 3
years
x + 29
years
After 3 years
20. What did we learn today?
1. The path of quadratic equation is parabolic
2. Real life examples of quadratic equations
3. The standard form of quadratic equation is ax2 + bx +c = 0
4. Representation of quadratic equation by given situations
