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anonymous
 4 years ago
0, 0, 4, 1+i find a polynomial function with integer coefficients that has the given zeroes
anonymous
 4 years ago
0, 0, 4, 1+i find a polynomial function with integer coefficients that has the given zeroes

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asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.0I a polynomial has roots \(x=r_1,x=r_2,x=r_3,...,x=r_n\) then it can be written as follows:\[(xr_1)(xr_2)(xr_3)...(xr_n)=0\]so, for the roots you have provided, we can write the polynomial as:\[\begin{align} (x0)(x0)(x4)(x(1i))&=0\\ \therefore (x)(x)(x4)(x1+i)&=0\\ \therefore x^2(x4)(x1+i)&=0\\ \therefore x^2(x^2x+ix4x+44i)&=0\\ \therefore x^2(x^25x+ix+44i)&=0\\ \therefore x^2(x^2(5i)x+4(1i))&=0\\ \therefore x^4(5i)x^3+4(1i)x^2&=0\\ \end{align}\]
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