Quadratic Equation



                   Quadratic Equation

A quadratic equation in the variable X is an equation of the form
where a,b and c are real numbers, a≠0 2x2+2x+5=0 is an quadratic equation, similarly 6x2+x+2=0, and

4x2-5x+2=0 are also quadratic equation.

Any equation in the form of p(x)=0 is a polynomial of degree 2,  is a quadratic equation. but when we write the terms of p(x) in descending order of their degree, then we get the standard form of the equation. That is, ax2+bx+c=0, a≠0, is called the standard form of quadratic equation.

Example:- (x-2)2+1=2x-3

Solution :-  

L.H.S=(x-2)2+1=x2-4x+4+1
                              
                          [(a-b)2= a2-2ab+b2]
          
           = x2-4x+5

Therefore, (x-2)2+1=2x-3 can be written as
                  
                     x2-4x+5=2x-3
                   
                     x2-4x+5-2x+3=0

i.e,                x2-6x+8=0

it is form ax2+bx+c=0,
therefore, the given equation is a quadratic equation.
  













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