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   Quadratic Equations - Class X
Formulae, Relations, Identities etc.
Quadratic Equation in one Variable
Definition: It is an equation of the form ax^2 + bx + c = 0 where a, b and c are real numbers and a is non zero. example  3x^2 - 5x + 7 = 0 

Standard form of a quadratic equation 
It is equation written in ascending or descending order of powers of the variable.
                                              Roots of a quadratic equation
A real number r is is root of quadratic equation  ax^2 + bx + c = 0, where a is non zero if   ar^2 + br + c = 0.

or

The values of variable satisfying the given quadratic equations are called its roots

Methods to find roots of a quadratic equation
1.   Factorisation Method
2.   Method of completing the squares
3.   Quadratic formula

 Discriminant
For a quadratic equation ax^2 + bx + c = 0, where a, b, c are real numbers and a is non zero. 
Discriminant (D) = b^2 - 4ac

Example of above
5x^2 + 4x - 11 = 0
Discriminant (D)        = b^2 - 4ac
                               = 4^2 - 4×5×( - 11)
                               = 16 + 220
                               = 236
Nature of roots
1.  If discriminant (D) > 0 - roots are real and distinct
2.  If D = 0                            -  roots are real and equal
3.  If D < 0                            -  no real roots
4.  If D > 0 and a perfect square and a, b, c are rational - roots are  
      real and distinct and rational
5.  If D > 0 , not a perfect square and a, b, c are rational - roots are
      real and distinct and form a conjugate pair

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