Chapter 2 · Polynomials

NCERT Exemplar Class 10 Maths Exercise 2.1

All 11 questions of NCERT Exemplar Class 10 Maths Exercise 2.1 (Polynomials), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   If ​one ​of ​the zeroes ​of the ​quadratic ​polynomial $(k-1)x^2+kx+1$ ​is $-3$, then the value of $k$ ​is

   1. (a)$\frac{4}{3}$
   2. (b)$\frac{-4}{3}$
   3. (c)$\frac{2}{3}$
   4. (d)$\frac{-2}{3}$
   Show answer

   (a) $\frac{4}{3}$

   Step-by-step solution →
2. Q2
   A quadratic polynomial, ​whose ​zeroes ​are $-3$ ​and $4$, ​is

   1. (a)$x^2-x+12$
   2. (b)$x^2+x+12$
   3. (c)$\frac{x^2}{2}-\frac{x}{2}-6$
   4. (d)$2x^2+2x-24$
   Show answer

   (c) $\frac{x^2}{2}-\frac{x}{2}-6$

   Step-by-step solution →
3. Q3
   If ​the zeroes ​of ​the quadratic ​polynomial $x^2+(a+1)x+b$ ​are 2 ​and $-3$, then

   1. (a)$a=-7,b=-1$
   2. (b)$a=5,b=-1$
   3. (c)$a=2,b=-6$
   4. (d)$a=0,b=-6$
   Show answer

   (d) $a=0,b=-6$

   Step-by-step solution →
4. Q4
   The ​number ​of ​polynomials having ​zeroes as $-2$ and $5$ ​is

   1. (a)$1$
   2. (b)$2$
   3. (c)$3$
   4. (d)more than $3$
   Show answer

   (d) more than $3$

   Step-by-step solution →
5. Q5
   Given that one of the ​zeroes of ​the cubic polynomial $a{x}^3+b{x}^2+cx+d$ is ​zero, the product of ​the ​other two ​zeroes ​is

   1. (a)$-\frac{c}{a}$
   2. (b)$\frac{c}{a}$
   3. (c)$0$
   4. (d)$-\frac{b}{a}$
   Show answer

   (b) $\frac{c}{a}$

   Step-by-step solution →
6. Q6
   If one of the zeroes of ​the ​cubic ​polynomial $x^3+a{x}^2+bx+c$ is $-1$, ​then ​the product ​of the other two zeroes is

   1. (a)$b-a+1$
   2. (b)$b-a-1$
   3. (c)$a-b+1$
   4. (d)$a-b-1$
   Show answer

   (a) $b-a+1$

   Step-by-step solution →
7. Q7
   The ​zeroes ​of the ​quadratic ​polynomial $x^2+99x+127$ are

   1. (a)both positive
   2. (b)both negative
   3. (c)one positive and one negative
   4. (d)both equal
   Show answer

   (b) both negative

   Step-by-step solution →
8. Q8
   The ​zeroes ​of ​the ​quadratic polynomial $x^2+kx+k$, $k\ne 0$,

   1. (a)cannot both be positive
   2. (b)cannot both be negative
   3. (c)are always unequal
   4. (d)are always equal
   Show answer

   (a) cannot both be positive

   Step-by-step solution →
9. Q9
   If the ​zeroes ​of the ​quadratic ​polynomial $a{x}^2+bx+c$, $c\ne 0$ ​are ​equal, ​then

   1. (a)$c$ and $a$ have opposite signs
   2. (b)$c$ and $b$ have opposite signs
   3. (c)$c$ and $a$ have the same sign
   4. (d)$c$ and $b$ have the same sign
   Show answer

   (c) $c$ and $a$ have the same sign

   Step-by-step solution →
10. Q10
    If one ​of the zeroes of a quadratic polynomial of the form $x^2+ax+b$ is ​the ​negative ​of ​the other, then ​it

    1. (a)has no linear term and the constant term is negative.
    2. (b)has no linear term and the constant term is positive.
    3. (c)can have a linear term but the constant term is negative.
    4. (d)can have a linear term but the constant term is positive.
    Show answer

    (a) has no linear term and the constant term is negative.

    Step-by-step solution →
11. Q11
    Which ​of ​the ​following is not ​the ​graph of a ​quadratic ​polynomial?

    1. (a)Graph (A)
    2. (b)Graph (B)
    3. (c)Graph (C)
    4. (d)Graph (D)
    Show answer

    (d) Graph (D)

    Step-by-step solution →