Types of quadratic equation and their difference
Quadratic equation:
An equation which having square of unknown (variable)
quantity, but no higher power is known as quadratic equation. The standard form
of quadratic equation in x variable is ax2+bx+c = o. whereas a is
the coefficient of x2, b is the coefficient of x and c is the
constant term. a,b,c all are real numbers and x is an known
variable.
For example
Standard
form example not
Standard form example
·
ax2+bx+c = o ax2+bx
= -c
·
4x2+3x+1 = o 4x2+3x=
-1
·
7x2+2x+8 = o 7x2+2x
= -8
·
x2-6x-9= o x2-6x
= 9
·
6x2-x+1= o 6x2
+1 = x
Pure quadratic equation:
Pure quadratic equation is form of quadratic equation in
which the term bx is absent.
It means in quadratic equation (ax2 + bx + c =
0), if b=0 then this equation is called pure quadratic equation. The form of
this equation is ax2 + c = 0 whereas a,b are real numbers and x is
known term called variable.
For example
·
ax2 + c = 0
·
5x2 + 6 = 0
·
px2 + q= 0
·
10x2 -10 = 0
·
2x2 - 18 = 0
Main difference b/w pure quadratic equation and quadratic equation.
The main difference b/w these two equations are the term bx.
·
It means if in any quadratic equation b=0 then
this time it is known as pure quadratic equation but if b=0 then this time it
is known as quadratic equation.
·
In pure quadratic equation the term bx is absent.
·
In pure quadratic equation the term bx is must be
present.
Methods to solve quadratic equation.
v
Factorization method
v
Completing square method
v
Quadratic formula
Methods to solve pure quadratic equation.
v factorization method
pure quadratic equation may be solved by using the property of square roots of equal numbers.
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