SOLUTION: how would i write a polynomial equation with rational coefficients in standard form with the given solutions of {{{sqrt(3) and 2i }}} so far I've gotten {{{ x-sqrt(3)=0 }}} {{{ x-2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: how would i write a polynomial equation with rational coefficients in standard form with the given solutions of {{{sqrt(3) and 2i }}} so far I've gotten {{{ x-sqrt(3)=0 }}} {{{ x-2      Log On


   

Question 529844: how would i write a polynomial equation with rational coefficients in standard form with the given solutions of sqrt%283%29+and+2i+ so far I've gotten +x-sqrt%283%29=0+ +x-2i=0+ then %28x-sqrt%283%29%29+%28x-2i%29+=o+ I'm not sure what to do after that.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
write a polynomial equation with rational coefficients in standard form with the given solutions of sqrt%283%29+and+2i+
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If it is going to have rational coefficients it must also have
as solutions -sqrt(3) and -2i.
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So you have:
f(x) = (x-sqrt(3))(x+sqrt(3))(x-2i)(x+2i)
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f(x) = (x^2-3)(x^2+4)
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f(x) = x^4+x^2-12
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cheers,
Stan H.