quadratic equation / chapter - 4 / class - 10 /Math / New St. Mery English School

Topics to be covered 

1- Need to quadratic equations in real life.

2-Recap (polynomial, equation, zeroes of a polynomial, relation between zeros of a polynomial, splitting of terms, completing the square method, quadratic formula, linear equation word problem

3- what is quadratic equation?

4- standard form of quadratic equation

5- Roots / zeroes/ solutions/poles of a quadratic equation

6- solving a quadratic equation

       a- factorization method

       b- completing the square method

       c- quadratic formula (sidharacharya law )

7- Nature of roots

8-word problems involving quadratic equation 

1- Need to quadratic equations in real life.

 1-It is used in tackling real life situation in the form of world problems.

2- It is used in solving puzzles

3- It is used in sports

4- It is used in study parabolic shape made by football 

2-Recap

term - The part of an algebraic expression which is the combination of variable and constant combined with multiply sign is called term 

Ex:- 6xy² , -4y² , 2x , 7x³y³z³       

Algebraic expression- The group of terms combined with plus ( + ) or minus ( - ) sign is called algebraic expression.

Ex:- 5y² + 2x – 3

             2x³ + 3x² – 4x + 8

Polynomial- An algebraic expresson whose powers are non-negative integer is called polynomial

Ex:- 5y² + 2x – 3

             2x³ + 3x² – 4x + 8

 Degree of a Polynomial - The highest power of a polynomial is called the degree of that given polynomial.

Ex:- 5y² + 2x – 3  |( Here the degree of polynomial is 2 )

             2x³ + 3x² – 4x + 8  ( Here the degree of polynomial is 3 )

There are four types of polynomial on the basis of degree

1- linear polynomial

2- quadratic polynomial

3- cubic polynomial

4- by-quadratic polynomial

What is equation?

Ans:- An equation is formed when two polynomials are combined by equal to sign ( = )

 What is quadratic equation?

Ans:- An equation that is in the form of  'quadratic polynomial = 0' than that equation is called quadratic equation.

Ex:- 5y² + 2x – 3 = 0

What is equation?

Ans:- An equation is formed when two polynomials are combined by equal to sign ( = )

 What is quadratic equation?

Ans:- An equation whose degree is 2 is called quadratic equation

                                                   or

An equation that is in the form of  'quadratic polynomial = 0' than that equation is called quadratic equation.

If p(x) is a quadratic polynomial than p(x) = 0 is a quadratic equation

 

 What is roots of the quadratic equation?

Ans:- Let p(x) = 0 is a quadratic equation, than the zeroes of the polynomials p(x) are called the roots of the equation p(x) = 0

or

variable का वह मान जिसे variable के स्थान पर रखने पर हमारा quadratic equation सटिस्फाय हो जाये तब वेरिएबल का वह मान ही roots of the quadratic polynomial कहलाता है 

therefore, x = ∝ is a root of p(x)=0, if and only if  p(∝) = 0