Q9 of 90 Page 2

Find all the zeroes of the polynomial given below having given numbers as its zeroes.

2x3 – 4x – x2 + 2;√2, – √2

2x3 – 4x – x2 + 2;√2, – √2


Given zeroes are √2 and – √2


So, (x – √2) and (x + √2) are the factors of 2x3 – 4x – x2 + 2


⟹ (x – √2)(x + √2) = x2 – 2 is a factor of given polynomial.


Consequently, x2 – 2 is also a factor of the given polynomial.


Now, let us divide 2x3 – 4x – x2 + 2by x2 – 2


The division process is



Here, quotient = 2x – 1


So, the zeroes is


Hence, all the zeroes of the given polynomial are , and


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