QUADRATIC EQUATION CONCEPT

                Quadratic equation concept            

     Topics.       

1.  What are Quadratic Equations?

2.  Roots of Quadratic Equation

3.  Methods to Solve Quadratic Equations

4.  Nature of Roots of quadratic equation

5.  Relationship Between Coefficients and Roots of Quadratic Equation

6. Finding a Quadratic Equation by roots 

7.  Solving a Quadratic Equation – Tips and Tricks

                                                                                 

 1. What is Quadratic Equation?   

Variable+ constant = terms 

                                          ⬇️

                                 polynomial

                                          ⬇️ 

                                 equation

                                          ⬇️ 

                                 degree 2

                                          ⬇️ 

                     Quadratic Equations 

The equation whose highest degree is two is called a quadratic equation . It is expressed in the form of:

ax² + bx + c =0 ( Standard form)

where x is the unknown variable and a, b and c are the constant terms ,a ≠ 0.

Example:

• 2x² – 64 = 0

• -2x² – 4 =0
• ( x-2 )² + 1 = 2x - 3
• x + 1/x = 2

                                                                               

2.  Roots of Quadratic Equation.     

●  The value of a variable for which the equation gets satisfied is called the solution or the root of quadratic equation. 

●  The number of roots of a polynomial equation is equal to its degree. 

Hence, a quadratic equation has 2  roots. 

The general form: ax² + bx + c = 0. Then α and β are the roots of quadratic equations.

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 3.  Methods to Solve Quadratic Equations

(1): Factorisation Method

(2): Quadratic Formula 

(3): Complete The Square Method 

(4): Graphical Method 

  4.  Nature of Roots of quadratic equation

VALUE OF DISCRIMINANT (  D )	NATURE OF ROOTS
b² – 4ac = 0	Real and equal
b² – 4ac > 0 (is a perfect square)	Real, rational and unequal
b2 – 4ac > 0 (is not a perfect square)	Real, Irrational and unequal
b² – 4ac < 0	Imaginary,

 5. Relationship Between Coefficients and Roots of Quadratic Equation.  

Quadratic Equation      ( ax² + bx + c = 0 )

Sum of roots.       (α+ β).   =     -b/a

Product of roots   (α. β)    = c/a

 6. Finding a Quadratic Equation by roots 

• If α and β are given roots then the Quadratic Equation:

X² - ( α + β ) X +  α. β  = 0

      

               OR

(X- α (X- β ) = 0