maths project abhi.pptx [autosaved]
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BY:-Abhishek.T.Raja
nClass:-10th DRoll no.:-33
Polynomials
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CONTENTS1. Introduction.
2. Zeroes of polynomials.
3. Relation between coefficients and zeroes of
polynomials.
4. Division Algorithm for Polynomials.
5. Summary.
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1.INTRODUCTION A polynomial is an expression constructed
from variables and constants using only the
operations of addition, subtraction, multiplication,
and non-negative integer exponents . However,
the division by a constant is allowed, because
the multiplicative inverse of a non-zero constant is
also a constant.For eg:-2x+7y, 3a+b, x+6
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Types of polynomial on the basis of degree The polynomial which has one degree is
called linear polynomial. for eg:-2x+3, 7x+9,
9x+13.
The polynomial which has two degree is called
quadratic polynomial. for eg:-2x2+3, 7x2+9.
The polynomial which has three degree is called
cubic polynomial. For eg:-x3+8, 3x3+45.
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2. Zeroes of polynomialsDefinition:- Take an equation 2x2+6x+4. Do it’s middle term splitting. = 2x2+(2+4)x+4 = 2x2+2x+4x+4 Take common in this equation = 2x(x+1)+4(x+1) Take common = (2x+4)(x+1)
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Let, 2x+4=0Then, 2x=-4 x=-4/2 x=-2Let, x+1=0 x=-1So ,we have two zeroes that is -4, -1.By this we can conclude that the number
replacing variable giving zero on doing mathematical operation is called zeroes of polynomial.
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We represent linear equation in the form ax2+by+c.Relation between coefficient and zeroes are:-a) Sum of zeroes of polynomial=-c/ab) Product of zeroes of polynomial=b/aIf one zero is α and second is β.a) α+ β=-c/ab) αβ=b/aSo this is the relation between coefficients and
zeroes of polynomial.
3. Relation between coefficients and zeroes of
polynomials.
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4. Division Algorithm for polynomial Division algorithm is a method by which we
can divide any two polynomial. Example :-
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5)Summary1) Polynomials of degree 1, 2 & 3 are called
linear, quadric and cubic polynomials respectively.2) A quadric polynomial can have at most two
zeros and a cubic polynomial can have three zeros.3) If we are given with the sum and product of
zeros we can find the polynomial by the following formula:
K[x2+(sum of zeros)x+(Product of zeros)]
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4) If two zeros of a polynomial are given then we can find the third zero by the following steps:
Convert the zeros into factors of the polynomial
Make a combined factor by multiplying the two
factors Now divide the polynomial by the combined
factor Write the quotient separately Do middle term splitting
By this process, we can find the third zero of the polynomial.
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Thank you and bye bye
……