Quadratic Formula

Quadratic Formula 

Quadratic Formula is also known as Shreedhracharya veedhi“.

 • What is Quadratic Formula ?

Quadratic Formula is a tool to find roots of any Quadratic equation instead of Middle term splitting method, Quadratic Formula can also be used to evaluate roots.

 •  Standard form of Quadratic equation is : 

     ax² + bx + c  


hence Quadratic Formula states as –
 

  •    x = [ -b ± √(b² – 4ac)]  / 2a



Quadratic

Qadratic


 • Discriminant:

Numerator part of this formula ( except “-b” ) known as discriminant, and gives a very useful information about nature of roots and denoted by “D” :

D = (b² – 4ac)

• following three conditions​ can be expected from Solution of D i.e.

  • if,  D > 0 then :  existed roots are real but                                    distinct
  • if,  D = 0 then :  existed roots are real and                                     equal
  • if,  D < 0 then :  roots doesn’t exist or                                           imaginary

 • From this test we can guess out what kind of roots any given Quadratic equation posses without evaluating.

 • Example :

Q. 2x² + 3x – 5
sol. by comparing from standard form of equation we have 
        a= 2 ; b= 3 ; c = -5
Test : with Discriminant 
            D = b² – 4ac
             = 3² – 4× 2×(-5)
             = 9  – (-40)
             = 9 +40  = 49 >0
means equation has real and distinct roots.
now by applying Quadratic Formula:
x = [ -3 ± (49)] / 2× 2
   = [ -3 ± 49 ] /4
by +value :
x = [-3 + 49] /4
   = 46/4  
by – value :
x = [ -3 – 49]/ 4
   = -52/4.
Hope this post has proven very useful for you, Do let me inform with comments, Feel free to share.
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