<PRE><B>Question 254301</B>
1. Determine all roots of P(x) = 3x^4+5x^3-9x^2-10x+8.
I had to graph it to find zeroes:
x = 1.6371972...
x = -2.409123
The other two roots seem to be complex.
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2. Determine all the roots of P(x) = 3x^5+5x^4+10x^3+14x^2+3x-3.
x = 1/3 is the only Real root
The other 4 roots seem to be complex.
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3. Determine a polynomial P(x) with real coefficients and of degree 5 for which three of its roots are x= -1, x = 1+2i and x= -3i. 
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Since the coefficients are Real x = 1-2i and x = +3i
are also roots
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P(x) = (x+1)((x-1)-2i)((x-1)+2i)(x-3i)(x+3i)
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P(x) = (x+1)((x-1)^2+4)(x^2+9)
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P(x) = (x+1)(x^2-2x+5)(x^2+9)
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Cheers,
Stan H.</PRE>