SOLUTION: Show that the polynomial f(z) = z^2 + 3/4z + 7 is factorizable over the complex field but not factorizable over real field

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Question 1114091: Show that the polynomial f(z) = z^2 + 3/4z + 7 is factorizable over the complex field but not factorizable over real field
Answer by amalm06(224) About Me  (Show Source):
You can put this solution on YOUR website!
f%28z%29=z%5E2%2B3%2F4z%2B7
=%281%2F4%29%284z%5E2%2B3z%2B28%29
=%281%2F64%29%28-8iz%2Bsqrt%28439%29-3i%29%288iz%2Bsqrt%28439%29%2B3i%29

Reference:http://www.wolframalpha.com/widget/widgetPopup.jsp?i0=x%5E4+-4x%5E3+%2B8x&id=15b128aa42d812ef9f3a9640bf1fb3fa&includepodid=Plot&p=v&podSelect&showAssumptions=1&showWarnings=&theme=gray&title=Factoring+Polynomials+Calculator