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

Division Algorithm
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

Division Algorithm
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,

Division Algorithm
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