Polynomial Class 10 Notes are provided here to help the class 10 students learn the syllabus topic in a more effective way. These notes are easy to understand and are given in a concise way. Apart from learning the concepts, students can also use this chapter 2 notes during revision and to quickly go through the important topics from this chapter. The highlight of these polynomials notes are-
- What is a polynomial?
- Type of polynomials
- Zeroes of a polynomial
- Division algorithm
- Example questions
- Practice questions
- Related polynomial articles
What is a Polynomial?
A polynomial is defined as an expression of two or more algebraic terms. The term polynomial itself means “poly” (means many) and “nomial” (means terms). A polynomial can consist of constants, variables, and even exponents. Check out this detailed polynomials article to understand about this topic it in detail and to get further information.
Standard Form of a Polynomial:
[a0 xn + a1 xn – 1 + a2 xn – 2 + …….. + an x2 + an – 1 x + an]
Degree of a Polynomial:
In a polynomial, the highest power of the polynomial is referred to as the degree of the polynomial.
Types of Polynomials
There are three main types of polynomials which are linear, quadratic, and cubic polynomial according to the degree of that polynomial.
|Degree||Type of Polynomial|
The above table can be explained as “a polynomial with degree 1 is known as a linear polynomial, a polynomial with degree 2 is binomial or quadratic polynomial, whereas with degree three is cubic polynomial.”
Root or Zeroes of a Polynomial
For any given polynomial, the value of x obtained by substituting the value of polynomial as 0 is known as the zero of the polynomial. These are also termed as roots of the equation.The Graphical meaning of the zeros of the polynomial is that the curve cuts the x-axis a point (k,0), where k is the root of the polynomial.
Notes: A polynomial of degree n will have n roots. So, any quadratic polynomial can only have a maximum of 2 zeroes and any cubic polynomial will have 3 zeroes maximum.
A quadratic equation ax2 + bx + c = 0 will have 2 roots, say α and β.
The sum of roots (α + β = -b⁄a)
Product of the roots (αβ = c⁄a)
According to division algorithm, any polynomial p(x) and any non-zero polynomial g(x), there exists polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x), where r(x) = 0 or degree r(x) < degree g(x).
Example 1 (based on zeroes or roots of a polynomial)
Example 2 (based on division algorithm)
- Find all the zeroes of
2x4 – 3x3 – 3x2 + 6x – 2 if two of its zeroes are √2, and -√2
Find all the zeroes of a polynomial 3x4 + 6x3 – 2x2 – 10x – 5 if two of its zeroes are given as: √(5⁄3), and -√(5⁄3)
Calculate the values of a, and b if the zeroes of the polynomial x3 – 3x2 + x + 1 are a – b, a, a + b.
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Related Polynomial Articles
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