Here you get the CBSE Class 10 Mathematics chapter 2, Polynomials: NCERT Exemplar Problems and Solutions (Part-I). This part of the chapter includes solutions for Exercise 2.1 of NCERT Exemplar Problems for Class 10 Mathematics Chapter: Polynomials. This exercise comprises of only the Multiple Choice Questions (MCQs) framed from various important topics in the chapter. Each question is provided with a detailed solution.
NCERT Exemplar problems are a very good resource for preparing the critical questions like Higher Order Thinking Skill (HOTS) questions. All these questions are very important to prepare for CBSE Class 10 Mathematics Board Examination 2017-2018 as well as other competitive exams.
Find below the NCERT Exemplar problems and their solutions for Class 10 Mathematics Chapter, Polynomials:
Multiple Choice Questions (MCQs)
Q. 1 If one of the zeroes of the quadratic polynomial (k – 1)x2 + kx +1 is −3 then the value of k is
We know that If α is the one of the zeroes of the quadratic polynomial f (x) = ax2 + bx + c then, f (α) must be equal to 0.
Given, −3 is one of the zeroes of the quadratic polynomial say (k – 1)x2 + kx +1.
Let’s take p(x) = (k – 1)x2 + kx +1
Then, p (−3) = 0
⟹ (k – 1)(−3)2 + k(−3)+1 = 0
⟹ 9(k – 1) − 3k + 1 = 0
⟹ 9k – 9 − 3k + 1 = 0
⟹ 6k – 8 = 0
⟹ k = 4/3
Q. 2 A quadratic polynomial, whose zeroes are -3 and 4, is
(a) x2 – x + 12
(b) x2 + x + 12
(c) x2/2 – x/2 − 6
(d) 2x2 + 2x − 24
Q.3 If the zeroes of the quadratic polynomial x2 + (a + 1) x + b are 2 and − 3, then
(a) a = − 7, b = − 1
(b) a = 5, b = − 1
(c) a = 2, b = − 6
(d) a = 0, b = − 6
Q.4 The number of polynomials having zeroes as −2 and 5 is
(d) More then 3
Q. 5 If one of the zeroes of the cubic polynomial is zero, the product of then other two zeroes is
Q. 6 If one of the zeroes of thee cubic polynomial is – 1 , then the product of the other two zeroes is
Q. 7 The zeroes of the quadratic polynomial x2 + 99 x + 127 are
(a) both positive
(b) both negative
(c) one positive and one negative
(d) both equal
Q. 8 The zeroes of the quadratic polynomial x2 + kx + k where, k ≠ 0.
(a) cannot both be positive
(b) cannot both be negative
(c) are always unequal
(d) are always equal
Q. 9 If the zeroes of the quadratic polynomial ax2 + bx + c where, c ≠ 0, are equal, then
(a) c and a have opposite signs
(b) c and b have opposite signs
(c) c and a have same signs
(d) c and b have the same signs
For equal root, b2 – 4ac = 0
⟹ b2 = 4ac
As b2 is always positive so 4ac must be positive, i.e. product of a and c must be positive i.e., a and c must have same sign either positive or negative.
Q. 10 If one of the zeroes of a quadratic polynomial of the form x2 + ax + b is the negative of the other, then it
(a) has no linear term and the constant term is negative
(b) has no linear term and the constant term is positive
(c) can have a linear term but the constant term is negative
(d) can have a linear term but the constant term is positive
Q. 11 Which of the following is not the graph of a quadratic polynomial?
Explanation: For a quadratic polynomial the curve must cross the X-axis on at most two points but in option (d) the curve crosses the X-axis on the three points, so it does not represent the quadratic polynomial.