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

• 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.
x = [ -3 ± (49)] / 2× 2
= [ -3 ± 49 ] /4
by +value :
x = [-3 + 49] /4
= 46/4
by – value :
x = [ -3 – 49]/ 4
= -52/4.
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