Answer :

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

So (x - √2) (x + √2) = x^{2} - 2

The above relation is same as (a + b) (a – b) = a^{2} – b^{2}

Here a = x and b = √2

The other zeroes are as follows:

2x^{2} – 3x + 1 = 0

Solving the above quadratic equation.

Sum = -3

Product = 2

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

2x^{2} – 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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