1. PIONEER COVENT
Name:- Rahul Singh Bhadauriya
Class:- 10th

2. POLYNOMIALS

3. WHAT IS A POLYNOMIAL?
A polynomial is an expression made with constants,
variables and exponents, which are combined using
addition, subtraction and multiplying but not division.
The exponents can only be o,1,2,3,4….. etc.
A polynomial cannot have infinite no. of terms.

4. DEGREE OF A
POLYNOMIAL
The exponent of highest degree term in a
polynomial is known as its degree.

5. CONSTANT POLYNOMIAL
A polynomial of degree zero is
called a constant polynomial.

6. LINEAR POLYNOMIAL
A polynomial of degree 1 is called a
linear polynomial.
ax+b=0

7. QUADRATIC POLYNOMIAL
A polynomial of degree 2 is called a
quadratic polynomial.
ax²+bx+c=0

8. CUBIC POLYNOMIAL
A polynomial of degree 3 is called a
cubic polynomial.
ax³ +bx²+cx+d=0

9. BI-QUADRATIC
POLYNOMIAL
A fourth degree polynomial is called a
bi-quadratic polynomial.
ax⁴+bx³+ cx²+ dx+e

10. VALUE OF A POLYNOMIAL
If ƒ(x) is a polynomial and α is any
real number, then the real number
obtained by replacing x by α in ƒ(x), is
called value of a polynomial.

11. ZEROES OF A POLYNOMIAL
A real number α is a zero of a polynomial
ƒ(x) if ƒ(α)=0.

12. RELATIONSHIP BETWEEN THE ZEROES
AND COEFFICIENTS OF A QUADRATIC
POLYNOMIAL
 Let α and β be the zeroes of the polynomial ax²+bx+c=0.
Sum of zeroes (α+β)= -b/a
= -(coefficient of x)/ coefficient of x²
Product of zeroes (αβ)= c/a
= constant term/ coefficient of x²

13. RELATIONSHIP BETWEEN THE ZEROES
AND COEFFICIENTS OF A CUBIC
POLYNOMIAL
 Let α, β and γ are the zeroes of the polynomial ax³+bx²+cx+d=0.
Sum of zeroes (α+β+γ)= -b/a
= -(coefficient of x²)/ coefficient of x³
αβ+βγ+γα=c/a
= coefficient of x/ coefficient of x³
Product of zeroes (αβγ)= -d/a
= -(constant term)/ coefficient of x³