# NCERT Class 10 Chapter 2 Polynomials Official CBSE Board Sample Problems Short Answer (For CBSE, ICSE, IAS, NET, NRA 2022)

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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

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

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

Sum = 8

Other =

Product =

Polynomial is

## 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 is less than 0

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