A quartic polynomial Q(x) with real coefficients has zeros 2+i and 3-2i, find the other two zeros.
There is a proof that all complex roots of
a polynomial equation with real constants will be complex conjugates to each other.
Therefore the answer is 2-i and 3+2i.
To find the other two zeros of the quartic polynomial Q(x) with given complex zeros, we can use the fact that complex roots come in conjugate pairs for polynomials with real coefficients.
Given that the zeros are 2+i, 3-2i, let's denote the other two zeros as a+bi and a-bi, where a and b are real numbers.
Since the coefficients are real, the conjugates of the zeros must also be zeros of the quartic polynomial. Therefore, the conjugates of 2+i and 3-2i are 2-i and 3+2i, respectively.
Hence, the four zeros of the quartic polynomial Q(x) are:
1) 2+i
2) 2-i
3) 3-2i
4) 3+2i