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
• 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.
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