If a radical be a zero of a polynomial then it's conjugate will also be the zero.
Like for the given problem has a zero 3+ √5. So, it's conjugate 3- √5 must be the other zero.
Hence, the zeroes of the polynomial are 1, 3+ √5 and 3-√5.
According to the problem, the degree of the polynomial is 4.
We already have three zeroes, so only one zero is unknown.
Because degree of polynomial = number of zeroes.
Other zeroes can be 1 and -3. We have already found that 3 - √5 is one of the zero.
So, A, B, C cannot be the correct choice.
But if 3+ √2 will be a zero then 3- √2 will also be the zero. Then the polynomial will have 5 zeroes which is not possible as the polynomial has degree four.
So, D: 3+ √2 cannot also be a zero of this polynomial.
Hope this helps you!
