Question 40991: Find a polynomial of the lowest degree with only real coeffiecients and having the given zeroes -4i and rad 7 Found 2 solutions by fractalier, astromathman:Answer by fractalier(6550) (Show Source):
You can put this solution on YOUR website! If one zero is -4i, then another must by 4i.
If one zero is sqrt(7), then another must be -sqrt(7).
Thus our polynomial starts as
(x - 4i)(x + 4i)(x - sqrt(7))(x + sqrt(7)) = 0
(x^2 + 16)(x^2 - 7) = 0
x^4 + 9x^2 - 112 = 0
You can put this solution on YOUR website! I disagree with fractalier's solution. For a polynomial to have real coefficients, the complex roots come in conjugate pairs, but real roots need not be paired. Therefore for the polynomial solution with the lowest degree the factors are:
so the polynomial is:
