SOLUTION: I actually have three questions. Two of the same type. Different numbers of roots, and I'm not even sure this is the right heading, but I couldn't find one that fit better, if you

Algebra ->  Algebra  -> Trigonometry-basics -> SOLUTION: I actually have three questions. Two of the same type. Different numbers of roots, and I'm not even sure this is the right heading, but I couldn't find one that fit better, if you       Log On

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 Click here to see ALL problems on Trigonometry-basics Question 254301: I actually have three questions. Two of the same type. Different numbers of roots, and I'm not even sure this is the right heading, but I couldn't find one that fit better, if you could help that would be great. If they're the same thing in the end, one being solved is fine, I just need a better explanation than the notes I was given for my online class. :(. The third question has imaginary numbers in it, and after a failed, and very irritating attempt I thought I would seek assistance. 1. Determine all roots of P(x) = 3x^4+5x^3-9x^2-10x+8. 2. Determine all the roots of P(x) = 3x^5+5x^4+10x^3+14x^2+3x-3. 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. Thank you!Answer by stanbon(57412)   (Show Source): You can put this solution on YOUR website!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. ------------------------------------------ 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. --------------------------------------------- 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. ---- Since the coefficients are Real x = 1-2i and x = +3i are also roots --------------------- P(x) = (x+1)((x-1)-2i)((x-1)+2i)(x-3i)(x+3i) --- P(x) = (x+1)((x-1)^2+4)(x^2+9) --- P(x) = (x+1)(x^2-2x+5)(x^2+9) ===================================== Cheers, Stan H.