2. Zeroes of polynomials.
3. Relation between coefficients and zeroes of
4. Division Algorithm for Polynomials.
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
Types of polynomial on the basis of
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.
2. Zeroes of polynomials
Definition:- Take an equation 2x2+6x+4.
Do it’s middle term splitting.
Take common in this equation
So ,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.
We represent linear equation in the form ax2+by+c.
Relation between coefficient and zeroes are:-
a) Sum of zeroes of polynomial=-c/a
b) Product of zeroes of polynomial=b/a
If one zero is α and second is β.
a) α+ β=-c/a
So this is the relation between coefficients and zeroes of
3. Relation between coefficients
and zeroes of polynomials.
4. Division Algorithm for polynomial
Division algorithm is a method by which we can divide
any two polynomial. Example :-
1) 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)]
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
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