If two zeros of a polynomial x 3 −3 x 2 +2   are 1+ 3   and 1− 3  , then find the third zero of the polynomial.

# If two zeros of a polynomial   are   and  , then find the third zero of the polynomial.

1. A

2. B

3. C

4. D

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### Solution:

Given polynomial   has two of its zeroes as   and  . We need to find the remaining zeroes.
By factor theorem, we have that if   is the zero of a polynomial, then   is the factor of that polynomial.
Since   and   are the two zeros of the polynomial, therefore, the respective factors are   and
Calculating the product of these factors we have,

Now dividing the given polynomial   by   we have,

Quotient obtained is  .
Equating the quotient equal to  , we have,

Hence, the remaining zero of the polynomial is  .
Therefore, option 1 is correct.

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