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 asand . 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