Writing Polynomial Functions from Complex Roots — Quiz

Question 3 • Mathematics III

Which polynomial function has a leading coefficient of 3 and roots negative 4 , i , and 2 , all with multiplicity 1 ?

Answer

f of x is equal to open paren x minus 3 close paren times open paren x plus 4 close paren times open paren x minus i close paren times open paren x minus 2 close paren

f of x is equal to open paren x minus 3 close paren times open paren x plus 4 close paren times open paren x minus i close paren times open paren x plus i close paren times open paren x minus 2 close paren

f of x is equal to 3 open paren x plus 4 close paren open paren x minus i close paren open paren x minus 2 close paren

f of x is equal to 3 open paren x plus 4 close paren open paren x minus i close paren open paren x plus i close paren open paren x minus 2 close paren

Explanation

A root r gives a factor of (x − r), so the roots −4, i, and 2 require the factors (x + 4), (x − i), and (x − 2). The leading coefficient of 3 means the product must also be multiplied by 3. Thus the function is 3(x + 4)(x − i)(x − 2), which is choice B.

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