BY:- SANJAY KUMAR MAHTOKAILASH ROY SARASWATI VIDYA MANDIR, JHUMRI TELAIYA(KODERMA)

The most general form of a n-degree polynomial is represented by:-

012

21

1 .........)( axaxaxaxaxp nn

nn

nn +++++= −

−−

−

011 ,,......., aaaa nn −,where n is a positive and ,where n is a positive and

are real numbers and are real numbers and oan ≠

1.Zeroes of a polynomial:- k is said to be zero of a polynomial if

2.Graph of a polynomial:-(a). Graph of a linear polynomial is a

straight line.(b) .Graph of a quadratic polynomial is a parabola open upwards like , if(c). Graph of a quadratic polynomial is a parabola open downwards like , if (d.) In general a polynomial of degree n

crosses the x-axis at atmost n points.

)(xp 0)( =kp

bax+

cbxaxxp ++= 2)(

cbxaxxp ++= 2)(

0>a

oa <)(xp

1.If are zeroes/roots of ,thenSum of roots

Product of roots

2.If are roots/zeroes of a quadratic polynomial ,then

βα , cbxaxxp ++= 2)(

2 oft coefficien

) oft coefficien(

x

x

a

b −=+⇒−=+= βαβα

2 oft coefficien

ermconstant t

xa

c =⇒== αβαβ

βα , )(xp

constant. a isk where

zeroes} ofproduct zeroes) of sum({)(

})({)( 2

2

+−=⇒++−=

xxkxp

xxkxp αββα