Find a polynomial with the given zeros.
$i , \sqrt { 7 } , - i$
A) $x ^ { 3 } - 7 x$
B) $x ^ { 3 } - \sqrt { 7 } x ^ { 2 } + x - \sqrt { 7 }$
C) $x ^ { 3 } - \sqrt { 7 } x ^ { 2 } + 7 x - \sqrt { 7 }$
D) $x ^ { 3 } - 7 x ^ { 2 } + x - 7$
E)none of these

Question

Find a polynomial with the given zeros. 
 $i , \sqrt { 7 } , - i$  
A)  $x ^ { 3 } - 7 x$
B) $x ^ { 3 } - \sqrt { 7 } x ^ { 2 } + x - \sqrt { 7 }$
C) $x ^ { 3 } - \sqrt { 7 } x ^ { 2 } + 7 x - \sqrt { 7 }$
D) $x ^ { 3 } - 7 x ^ { 2 } + x - 7$
E)none of these

Quizplus · Accepted Answer

The correct answer is B because the polynomial with the given zeros is $x ^ { 3 } - \sqrt { 7 } x ^ { 2 } + x - \sqrt { 7 }$. This can be verified by plugging in the given zeros into the polynomial and checking that the result is zero.

Find a Polynomial with the Given Zeros i,7,−ii , \sqrt { 7 } , - ii,7​,−i

Find a Polynomial with the Given Zeros $i , \sqrt { 7 } , - i$