Question 665655: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree: 4; zeros: 2i and -5i
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! Complex roots occur in pairs, ie + or - 2i and + or - 5i.
Your four (for 4th order polynomial) factors are
(1) f(x) = (x+2i)(x-2i)(x+5i)(x-5i) which multiplies (FOIL) to
(2) f(x) = (x^2+4)*(x^2+25) or
(3) f(x) = x^4 + 29x^2 + 100
Note the real coefficients result from the use of complex pairs.
Also note that (2i)*(-2i) = -4(i)^2, but i^2 = -1, so (2i)*(-2i) = +4.
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