Here we are providing Quick Revision Notes, Common mistakes we do while solving problems and Types of questions asked in Polynomials for Class 10 Maths. Students are advised to check out these points to score better in exams.
Quick Revision Notes for Class 10 Maths Chapter 2 Polynomials
- A polynomial p(x) in one variable x is an algebraic expression in x of the form p(x) = anxn + an–1xn–1 + … + a2x2 + a1x + a0 where an, an–1, …, a0 are real numbers with an ≠ 0.
- The highest power of x in p(x) is called the degree of the polynomial p(x).
- A quadratic polynomial in x with real coefficients is of the form ax2 + bx + c, where a, b, c are real numbers with a≠0
- A polynomial p(x) of degree n has atmost n zeroes.
- A real number k is said to be a zero of a polynomial p(x) if p(k) = 0.
- A polynomial may have no zero, one or more than one zeroes.
- Let p(x) be a polynomial in x and k be any real number, then the value obtained by replacing x by k in p(x) is called the value of p(x) at x = k and is denoted by p(k).
- 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.
- If a and b are the zeroes of the quadratic polynomial ax2 + bx + c, then α + β = −b/a, αβ = c/a.
- If α, β are zeroes of the quadratic polynomial p (x), then p(x) = x2 – (α + β) x + αβ
Common mistakes we do while solving problems.
We are listing common mistakes we do while solving polynomials problems. Take care of these points to avoid these common errors and score better marks in maths.
(1) Error: Doing mistakes in finding zeroes of a polynomial from graph.
Correction: Remember that x-coordinate(s) of point(s), where the graph of given polynomial intersects the x-axis are zeroes of the polynomial.
(2) Error: Splitting the middle term of a polynomial incorrectly to find the zeroes.
Correction: To split b of the polynomial ax2 + bx + c, write b as the sum of two numbers whose product is ac.
(3) Error: Finding incorrectly p(x) at x = k.
Correction: To find p(x) at x = k, replace x by k in p(x) carefully and get the answer.
(4) Error: Forming incorrectly a quadratic polynomial when zeroes are a, b as (x – α) (x – β). Correction: Form a quadratic polynomial with zeroes a, b as k (x – α) (x – β), where k is real.
Types of Questions Asked:
There are mainly three types on which the questions are asked in exams. Students are advised to solve problems based on these types to score better marks in exams.
- To find the zeroes of the quadratic polynomial and the relation between the zeroes and its coefficients.
- To form a quadratic polynomial with given sum of zeroes and product of zeroes.
- To find all the zeroes of a polynomial if some of the zeroes are given.