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if in equation
A=C, then?
two roots α and β are reciprocal to each other

if in equation
B=0, then?
two roots α and β are equal in magnitude and oposite in sign

in equation x^{2}+5x+6=0
the sign of two roots α and β is ???
 sign of (α and β)= ve
 sign of (αβ)= +ve
 both roots α and β are negative

in equation x^{2}5x+6=0
the sign of two roots α and β is ???
 sign of (α and β)= +ve
 sign of (αβ)= +ve
 so,both roots α and β are positive

in equation x^{2}5x6=0
the sign of two roots α and β is ???
 sign of (α and β)= +ve
 sign of (αβ)= ve
 then, α is positive and β is negative if α>β(numerically)

in equation x^{2}+5x6=0
the sign of two roots α and β is ???
 sign of (α and β)= ve
 sign of (αβ)= +ve
 then, α is negative and β is positive
 if, α>β(numerically)

roots of an equation is given by
x=(b±√D)÷2a

Nature Of Roots:
If, D<0
complex with non zero imaginary part

Nature Of Roots:If,
D=0
rational and equal

Nature Of Roots:If,
D>0 and is a perfect square
rational and unequal

Nature Of Roots:If,
D>0 and is NOT a perfect square
irrational and conjugate pairs

if in equation
A=1, and B,C are integers
and
roots are rational numbers
these roots must be integers

if in equation
and
one root is common, then

condition that , is factorizable into two linear factors
when D 0

formation of a quadratic equation??

nature of roots ??
If D<0 then ???
and D 0 then ,
 D<0 Imaginary
 D0 Real

