Select from the following which is the polynomial of degree n that has the given zero(s).
Zeros
Degree $x = 0 , \sqrt { 5 } , - \sqrt { 5 }$ $$n = 3$$

A) $f ( x ) = x ^ { 3 } + \sqrt { 5 } x$
B) $f ( x ) = x ^ { 3 } + 5 x$
C) $f ( x ) = - x ^ { 3 } - 5 x$
D) $f ( x ) = x ^ { 3 } - \sqrt { 5 } x$
E) $f ( x ) = x ^ { 3 } - 5 x$

Question

Select from the following which is the polynomial of degree n that has the given zero(s). ​
Zeros
Degree $x = 0 , \sqrt { 5 } , - \sqrt { 5 }$ $$n = 3$$ ​
​
A) $f ( x ) = x ^ { 3 } + \sqrt { 5 } x$
B) $f ( x ) = x ^ { 3 } + 5 x$
C) $f ( x ) = - x ^ { 3 } - 5 x$
D) $f ( x ) = x ^ { 3 } - \sqrt { 5 } x$
E) $f ( x ) = x ^ { 3 } - 5 x$

Quizplus · Accepted Answer

Given zeros are $x = 0, \sqrt{5}, -\sqrt{5}$. The polynomial with these zeros is $f(x) = x(x - \sqrt{5})(x + \sqrt{5}) = x(x^2 - 5) = x^3 - 5x$, which matches option E.

Select from the Following Which Is the Polynomial of Degree x=0,5,−5x = 0 , \sqrt { 5 } , - \sqrt { 5 }x=0,5​,−5​

Select from the Following Which Is the Polynomial of Degree $x = 0 , \sqrt { 5 } , - \sqrt { 5 }$