Polynomials Class 9 Extra Questions
Question 1: Find the value of x in the polynomial equation 2x2 – 5x + 3 = 0.
Solution:
We can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b2 – 4ac)) / 2awhere a = 2, b = -5, and c = 3.
Substituting the values:
x = (5 ± √(25 – 423)) / 2*2
x = (5 ± √(25 – 24)) / 4
x = (5 ± √1) / 4
So, the solutions are:
x = (5 + 1) / 4 = 6 / 4 = 3/2
and x = (5 – 1) / 4 = 4 / 4 = 1.
Question 2: Factorize the polynomial x2 – 4x + 4.
Solution:
We observe that the given polynomial is a perfect square trinomial.
It can be written as (x – 2)2.
So, the factored form is (x – 2)(x – 2) or (x – 2)2.
Question 3: Find all the roots of the polynomial equation x^3 – 6x^2 + 11x – 6 = 0.
Solution:
We can use synthetic division or polynomial long division to factorize the polynomial and find its roots.
After factorizing, we find that the roots are x = 1, x = 2, and x = 3.
Question 4: Given the polynomial 3x4 – 7x3 + 2x2 – 5x + 1, find its degree and leading coefficient.
Solution:
The degree of a polynomial is the highest power of the variable present. In this case, the degree is 4. The leading coefficient is the coefficient of the term with the highest power of the variable. Here, the leading coefficient is 3.
Question 5: Simplify the expression (2x2 – 3x + 1)(x2 + 4x – 2).
Solution:
We use the distributive property to expand the expression:
(2x2 – 3x + 1)(x2 + 4x – 2) = 2x2(x2+4x−2)−3x(x2+4x−2)+1(x2+4x−2)
= 2x4+8x3−4x2−3x3−12x2+6x+x2+4x−2
= 2x4 + 5x3 – 15x2 + 10x – 2
Polynomials – Definition, Standard Form, Types, Identities, Zeroes
Polynomials: In mathematics, polynomials are mathematical expressions consisting of indeterminates (also called variables) and coefficients, that involve only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. They are used in various fields of mathematics, astronomy, economics, etc. There are various examples of the polynomials such as 2x + 3, x2 + 4x + 5, etc.
In this article, we will learn about, Polynomials, Degrees of Polynomials, Examples of Polynomials, Zeros of Polynomials, Polynomial Equations, and others in detail.
Table of Content
- What are Polynomials?
- Polynomials Definition
- Polynomials Examples
- Characteristics of Polynomials
- Standard Form of a Polynomial
- Degree of a Polynomial
- Degree of Single Variable Polynomial
- Degree of a Multivariable Polynomial
- Terms in a Polynomial
- Types of Polynomials
- Properties of Polynomials (Theorems of Polynomials)
- Operations on Polynomials
- Addition of Polynomials
- Subtraction of Polynomials
- Multiplication of Polynomials
- Division of Polynomials
- Factorization of Polynomials
- Methods of Factorization of Polynomial
- Greatest Common Factor (GCF)
- Substitution Method
- Grouping Method
- Difference of Two Squares Identity
- Zeros of Polynomial
- How to Find Zeros of Polynomials?
- Linear Polynomial
- Quadratic Polynomial
- Cubic Polynomial
- Higher Degree Polynomial
- Polynomial Identities
- Polynomial Equations
- Solving Polynomials
- Polynomial Functions
- Polynomials Class 9 Extra Questions
- Polynomials Class 10 Extra Questions
- Practice Problems on Polynomial
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