Exercise 2.2

Question 1:

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

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

Question 2:

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

 

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  .

Let the polynomial be  .

Therefore, the quadratic polynomial is .