In this article you will get CBSE Class 10 Mathematics chapter 2, Polynomials: NCERT Exemplar Problems and Solutions (Part-IV). Every question has been provided with a detailed solution. All the questions given in this article are very important to prepare for CBSE Class 10 Board Exam 2017-2018.
Find below the NCERT Exemplar problems and their solutions for Class 10 Mathematics Chapter, Polynomials:
Exercise 2.4
Long Answer Type Questions
Q. 1 For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also, find the zeroes of these polynomials by factorisation.
NCERT Exemplar Solution for CBSE Class 10 Mathematics Chapter: Polynomials (Part-III)
Main concept for solving the above questions is:
- If α and β are the two zeroes of a polynomial then that polynomial can be expressed as:
f (x) = x2 – (α + β)x + αβ
Or f (x) = x2 – (Sum of roots, S)x + (Product of roots, P)
- Then the quadratic polynomial so formed will be factorised by splitting the middle term to obtain the required zeroes.
Q. 2 If the zeroes of the cubic polynomial x3 – 6x2 + 3x +10 are of the form a, a + b and a + 2b for some real number a and b, find the values of a and b as well as the zeroes of the given polynomial.
Solution.
Q. 4 Find k so that x2 + 2x + k is a factor of 2x4 + x3 – 14x2 + 5x + 6. Also, find all the zeroes of the two polynomials.
Solution.
Q. 6 For which values of a and b, the zeroes of q(x) = x3 + 2x2 + a are also the zeroes of the polynomial p(x) = x5 − x4 − 4x3 + 3x2 + 3x + b. Which zeroes of p(x) are not the zeroes of q(x)?
Solution.
Given that zeroes of q(x) = x3 + 2x2 + a are also the zeroes of the polynomial p(x) = x5 − x4 − 4x3 + 3x2 + 3x + b, it means q(x) is a factor of p(x) .
By using division algorithm,
