In this page 'Problems on algebra-II' we are going to see problems on zeros of the polynomial and roots of the equation.

Parents and teachers can guide the students to do the problems on their own. If they are having any doubt they can verify the solutions. Before going to problems we will recall some definitions of polynomials about the type, degree, zeros and roots of the equation.

** Types of polynomials**

* Based on the degree:*

- Constant polynomial: A polynomial of degree zero is called a constant polynomial.
- Linear polynomial: A polynomial of degree one is called a linear polynomial.
- Quadratic polynomial: A polynomial of degree two is called a quadratic polynomial.
- Cubic polynomial: A polynomial of degree three is called a cubic polynomial.

* Based on the terms:*** **

- Monomial : Polynomials which have only one term are known as monomials.
- Binomial: Polynomials which have only two terms are called binomials.
- Trinomial: Polynomials which have three terms are called trinomials.

** Zeros of the polynomial**

Let p(x) be a polynomial in x. If p(a) = 0, then we say that a is a zero of the polynomial p(x).

** Roots of a polynomial equation**

If x=a satisfies the polynomial equation p(x)=0, then x=a is called a root of the polynomial equation p(x)=0.

The following problems are based on zeros of the polynomials.

1. Find the zeros of the following polynomials

(i) p(x) = 4x-1

(ii) p(x) = 3x+5

(iii) p(x) = 2x

(iv) p(x) = x+9

The following problems are based on roots of the polynomial equations.

2. Find the roots of the following polynomial equations.

(i) x-3 = 0

(ii) 5x-6 = 0

(iii) 11x +1 = 0

(iv) -9x = 0

3. Verify whether the following are roots of the polynomial equations indicated against them.

(i) x² - 5x +6 = 0: x= 2,3

(ii) x² +4x+3 = 0: x= -1,2

(iii) x³ - 2x² -5x +6 = 0: x = 1, -2,3

(iv) x³ - 2x² -x +2 = 0: x = -1,2,3

Students can try to solve the problems on their own. Parents and teachers can encourage the students to do so. If they are having any doubt they can verify the solutions. If you are having any further doubt you can contact us through mail, we will help you to clear your doubt.