Q3 of 108 Page 38

With the following polynomials their zeroes are given. Find their all other zeroes:


Given that √2 and -√2 are the zeroes of the given polynomial.

So (x - √2) (x + √2) = x2 - 2


The above relation is same as (a + b) (a – b) = a2 – b2


Here a = x and b = √2



The other zeroes are as follows:


2x2 – 3x + 1 = 0


Solving the above quadratic equation.


Sum = -3


Product = 2


So the numbers which satisfy the above condition are -2 and -1


2x2 – 2x - x + 1 = 0


2x(x – 1) – 1(x – 1) = 0


(2x – 1) (x – 1) = 0


Solving the first part,


2x-1 = 0


2x = 1


x = 1/2


Solving the second part,


x – 1 = 0


x = 1


Therefore the other zeroes of the polynomials are 1/2 and 1.


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