# NCERT Class 10 Chapter 2 Polynomials Official CBSE Board Sample Problems Short Answer

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## Question

**An NGO decided to distribute books and pencils to the students of a school running by some other NGO. For this they collected some amount from different people. The total amount collected is represented by** **. From this fund each student received an equal amount. The number of students, who received the amount, is represented by** **. After distribution,** **, amount is left with the NGO which they donated to school for their infrastructure. Find the amount received by each student from the NGO. What value has been depicted here?**

### Solution

The total amount collated,

Number of students,

*Let* amount received by each students, *q(x).*

Amount left after distribution,

by using division algorithm, we have

Amount received by each student,

Value: humanity and socialism

## Question

**Divide the polynomial** **and find the quotient and the remainder. Also verify the division algorithm.**

### Solution

Let

Now, quotient

Remainder

By division algoritithm

Hence division algorithm is verifed.

## Question

**Quadratic poIynomiaI** **has zeroes as****and . Now term a quadrille polynomial whose zeroes ase** **and****.**

### Solution

and are the zeroes of the polynomial

Now, zeroes of the required polynomial arc and

Now, required polynomial is p

Where k be any constant.

## Question

**On dividing** **by a polynomial g(x), the quotient and the remainder were**

**and 6 respectively. Find 9(x).**

### Solution

Consider Divided:

Quotient

Remainder r*(x) =*6 and divisor is g(x)

Applying division algorithm, we get

So,

## Question

**Find the zeroes of the quadratic polynomial** **and verity the relationship between the zeroes and the coefficients.**

### Solution

Given quadratic polynomial is

Consider

For zeroes of polynomial p(x), put p(x) 0.

Hence zeroes of polynomial *p(x)* are and -

Here and

Here sum of zeroes

Product of zeroes

Also from the polynomial

Sum of zeroes

Product of zeroes=

These verify the relation. _______- ______

## Question

**If the zeroes of a polynomial****, are the HCF of** **then find the value of k.**

### Solution

Given, HCF of is one of the roots.

## Question

**Find the zeros of the quadratic polynomial** **and verify the relationship between the zeroes and the coefficients**.

### Solution

). Zeroes are 6 and

## Question

**Find the quadratic polynomial whose sum of the zeroes is 8 and one zero is**

### Solution

Sum = 8

Other=

Product=

Polynomial ¡s

## Question

**If one zero of the polynomial** **is reciprocal of the other, find the value of a.**

### Solution

Zeroes are reciprocals of each other so the product of the zeroes is 1

## Question

**At how many points will the polynomial** **intersect the x-axis?**

### Solution

It will intersect the x axis at only one point as

Has no zeroes as its discriminant ¡s less than 0