Updated By SaraNextGen

On April 21, 2024, 11:35 AM

Exercise 2.2 (Revised) - Chapter 2 - Polynomials - Ncert Solutions class 10 Maths

Question 1:

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

Answer:

The value of  is zero when x − 4 = 0 or x + 2 = 0, i.e., when x = 4 or x = −2

Therefore, the zeroes of  are 4 and −2.

Sum of zeroes = 

Product of zeroes 

The value of 4s² − 4s + 1 is zero when 2s − 1 = 0, i.e.,

Therefore, the zeroes of 4s² − 4s + 1 are and .

Sum of zeroes = 

Product of zeroes 

The value of 6x² − 3 − 7x is zero when 3x + 1 = 0 or 2x − 3 = 0, i.e.,  or

Therefore, the zeroes of 6x² − 3 − 7x are .

Sum of zeroes = 

Product of zeroes = 

The value of 4u² + 8u is zero when 4u = 0 or u + 2 = 0, i.e., u = 0 or u = −2

Therefore, the zeroes of 4u² + 8u are 0 and −2.

Sum of zeroes = 

Product of zeroes = 

The value of t² − 15 is zero when   or  , i.e., when 

Therefore, the zeroes of t² − 15 are   and .

Sum of zeroes =

Product of zeroes = 

The value of 3x² − x − 4 is zero when 3x − 4 = 0 or x + 1 = 0, i.e., when   or x = −1

Therefore, the zeroes of 3x² − x − 4 are  and −1.

Sum of zeroes = 

Product of zeroes 

Question 2:

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

Answer:

Let the polynomial be  , and its zeroes be  and  .

Therefore, the quadratic polynomial is 4x² − x − 4.

Let the polynomial be  , and its zeroes be  and  .

Therefore, the quadratic polynomial is 3x² −  x + 1.

Let the polynomial be  , and its zeroes be  and  .

Therefore, the quadratic polynomial is  .

Let the polynomial be  , and its zeroes be  and  .

Therefore, the quadratic polynomial is  .

Let the polynomial be  , and its zeroes be  and  .

Therefore, the quadratic polynomial is  .

Let the polynomial be  .

Therefore, the quadratic polynomial is .