**EXERCISE 1**

Question: 1. The graphs of y = p(x) are given below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.

(i)

**Answer:-**Number of zeroes = 0, since the line is not intersecting the x-axis

(ii)

**Answer:-**Number of zeroes = 1, since the line intersects the x axis once.

(iii)

**Answer:-**Number of zeroes = 2, since the line intersects the x axis twice.

(iv)

**Answer:-**Number of zeroes = 2

(v)

**Answer:**Number of zeroes = 4

(vi)

**Answer:**Number of zeroes = 2

## NCERT Solution - Exercise 2.2

Question – 1 - Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

Answer:

Hence, zeroes are -2 and 4

We know that;

Again we know that;

From sum and product of zeroes, the relationship between the zeroes and coefficients is verified.

Answer:

We know that;

We know that;

From sum and product of zeroes, the relationship between the zeroes and coefficients is verified.

Answer:

We know that;

We know that;

From sum and product of zeroes, the relationship between the zeroes and coefficients is verified.

Answer:

We know that;

We know that;

From sum and product of zeroes, the relationship between the zeroes and coefficients is verified.

Answer:

We know that;

We know that;

From sum and product of zeroes, the relationship between the zeroes and coefficients is verified.

Answer:

We know that;

We know that;

From sum and product of zeroes, the relationship between the zeroes and coefficients is verified.

Question – 2 - Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

Answer: We know that a quadratic equation can be given as follows:

Hence; the required equation can be written as follows:

Answer: We know that a quadratic equation can be given as follows:

Hence; the required equation can be written as follows:

Hence; the required equation can be written as follows:

Answer: We know that a quadratic equation can be given as follows:

Hence; the required equation can be written as follows:

Answer: We know that a quadratic equation can be given as follows:

Hence; the required equation can be written as follows:

Answer: We know that a quadratic equation can be given as follows:

Hence; the required equation can be written as follows:

Answer: We know that a quadratic equation can be given as follows:

Hence; the required equation can be written as follows:

## NCERT Solution - Exercise 2.3

Question – 1 - Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

Answer:

Here; quotient = x – 3 and remainder = 7x – 9

Answer:

Answer:

Question – 2 - Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:

Answer:

Here, the first polynomial is a factor of the second polynomial.

Answer:

Here, the first polynomial is a factor of the second polynomial.

Answer:

Here, the first polynomial is not a factor of the second polynomial.

Question – 3 - Obtain all other zeroes of if two of its zeroes are

Answer: A quadratic equation can be given as follows:

Hence, if roots are then the equation can be written as follows:

Given polynomial is divided by this equation as follows:

Hence,

Roots for the equation can be calculated as follows:

Question – 4 - On dividing by a polynomial g(x), the quotient and remainder were respectively. Find g(x).

Answer: Subtracting the remainder from the given polynomial we get;

Dividing equation (1) by quotient will give the value of g(x)

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