CBSE Class 10 Maths Revision Notes Chapter 2 Polynomials
- Geometrical Meaning of the Zeroes of a Polynomial
- Zeroes and Coefficients of a Polynomial
- Division Algorithm for Polynomials
- Monomials: Algebraic expression with one term is known as Monomial.
- Binomial: Algebraic expression with two terms is called Binomial.
- Trinomial: Algebraic expression with three terms is known as Trinomial.
- Polynomials: All above mentioned algebraic expressions are called Polynomials.
- Polynomials of degrees 1, 2 and 3 are called linear, quadratic and cubic polynomials respectively.
- A quadratic polynomial in x with real coefficient is of the form ,where a, b, c are real numbers with .
- The zeroes of a polynomial p(x) are precisely the x–coordinates of the points where the graph of y = p(x) intersects the x-axis i.e. x = a is a zero of polynomial p(x) if p(a) = 0.
- A polynomial can have at most the same number of zeros as the degree of polynomial.
- For quadratic polynomial
Sum of zeroes =
Product of zeroes =
10. In a cubic polynomial , if are the zeroes of the polynomial, then
11. The division algorithm states that given any polynomial p(x) and polynomial g(x), there are polynomials q(x) and r(x) such that :
where r(x) = 0 or degree of r(x) < degree of g(x).
Or Dividend = Divisor x Quotient + Remainder
If r(x) = a zero polynomial, then p(x) is said to be completely divisible by g(x), i.e., g(x) is a factor of p(x).