NCERT Solutions for Class 10 Math Chapter 2 - Polynomials

Question 1:

The graphs of y = p(x) are given in figure below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.

Question 2:

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

1. x² - 2x - 8
2. 4s² - 4s + 1
3. 6x² - 3 - 7x
4. 4u² + 8u
5. t² - 15
6. 3x² - x - 4

Question 3:

Question 4:

Question 5:

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial.

1. t² - 3, 2t⁴ + 3t³ - 2t² - 9t - 12
2. x² + 3x + 1, 3x⁴ + 5x³ - 7x² + 2x + 2
3. x³ - 3x + 1, x⁵ - 4x³ + x² + 3x + 1

Question 6:

Question 7:

On dividing x³ - 3x² + x + 2 by a polynomial g(x), the quotient and remainder were x - 2 and -2x + 4 respectively, find g(x).

Question 8:

Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and

1. deg p(x) = deg q(x)
2. deg q(x) = deg r(x)
3. deg q(x) = 0

Question 9:

Give examples of polynomials p(x), g(x), q(x)
and r(x), which satisfy the division algorithm and

1. deg p(x) = deg q(x)
2. deg q(x) = deg r(x)
3. deg q(x) = 0

Question 10:

Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, –7, –14 respectively.

Question 11:

Question 12:

Question 13:

Question 14:

If one of the zeroes of the quadratic polynomial (k – 1)x² + kx + 1 is –3, then the value of k is:

Question 15:

A quadratic polynomial, whose zeroes are –3 and 4, is:

1. x² – x + 12
2. x² + x + 12
3. 
4. 2x² + 2x – 24

Question 16:

If the zeroes of the quadratic polynomial x² + (a + 1) x + b are 2 and –3, then:

1. a = –7, b = –1
2. a = 5, b = –1
3. a = 2, b = –6
4. a = 0, b = –6

Question 17:

The number of polynomials having zeroes as
–2 and 5 is

1. 1
2. 2
3. 3
4. more than 3

Question 18:

Given that one of the zeroes of the cubic polynomial ax³ + bx² + cx + d is zero, the product of the other two zeroes is:

1. 
2. 
3. 0
4. 

Question 19:

If one of the zeroes of the cubic polynomial x³ + ax² + bx + c is –1, then the product of the other two zeroes is:

1. b – a + 1
2. b – a – 1
3. a – b + 1
4. a – b – 1

Question 20:

The zeroes of the quadratic polynomial x² + 99x + 127 are:

1. both positive
2. both negative
3. one positive and one negative
4. both equal

Question 21:

The zeroes of the quadratic polynomial x² + kx + k, k $\ne$ 0;

1. cannot both be positive
2. cannot both be negative
3. are always unequal
4. are always equal

Question 22:

If the zeroes of the quadratic polynomial ax² + bx + c, c $\ne$ 0 are equal, then:

1. c and a have opposite signs
2. c and b have opposite signs
3. c and a have the same sign
4. c and b have the same sign

Question 23:

If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it:

1. has no linear term and the constant term is negative
2. has no linear term and the constant term is positive
3. can have a linear term but the constant term is negative
4. can have a linear term but the constant term is positive

Question 24:

Can x² – 1 be the quotient on division of x⁶ + 2x³ + x – 1 by a polynomial in x of degree 5?