POLYNOMIALS OF CLASS 10
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Transcript of POLYNOMIALS OF CLASS 10
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BY:- SANJAY KUMAR MAHTOKAILASH ROY SARASWATI VIDYA MANDIR, JHUMRI TELAIYA(KODERMA)
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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 ≠
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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
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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
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