SOLUTION: write a polynomial function with rational coefficients so that P(x)=0 has the given roots.put in standard form. 1). sqrt(3), 2i

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: write a polynomial function with rational coefficients so that P(x)=0 has the given roots.put in standard form. 1). sqrt(3), 2i      Log On


   

Question 715732: write a polynomial function with rational coefficients so that P(x)=0 has the given roots.put in standard form.
1). sqrt(3), 2i
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Rational coefficients?

%28x%2Bsqrt%283%29%29%28x-sqrt%283%29%29%28x%2B2i%29%28x-2i%29=0, It MUST be at least a degree 4 function. The trick is to not be mislead when seeing only the two listed roots.

Do the multiplying for those four binomials:
%28x%5E2-3%29%28x%5E2-4%29=0

Do the rest of the multiplying if you want general form:
x%5E4-3x%5E2-4x%5E2%2B12=0
highlight%28x%5E4-7x%5E2%2B12=0%29
Or if you prefer,
highlight%28P%28x%29=x%5E4-7x%5E2%2B12%29