How do you write a polynomial in standard form given the zeros (5 ,+i√3 , -i√3)?

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Answer 1 · 2016-03-25T09:29:48

#f(x))=x^3-5x^2+9x-45#

A polynomial with zeros #{a,b,c}# is given by #f(x)=(x-a)(x-b)(x-c)#.

As the zeros are #{5,+isqrt3,-isqrt3}#,

#f(x)=(x-5)(x-isqrt3)(x-(-isqrt3))=(x-5)(x-isqrt3)(x+isqrt3)# or

#f(x)=(x-5)(x^2-(isqrt3)^2)# or

#f(x)=(x-5)(x^2-(-9))=(x-5)(x^2+9)# or

#f(x)=x(x^2+9)-5(x^2+9)=x^3+9x-5x^2-45# or

#f(x))=x^3-5x^2+9x-45#