Find a polynomial with the given zeros. $0,0,0 , \sqrt { 3 } , - \sqrt { 3 }$
A) $x ^ { 5 } - 3 x ^ { 3 }$
B) $x ^ { 5 } - 6 x ^ { 3 }$
C) $x ^ { 5 } - x ^ { 3 } + 3$
D) $x ^ { 2 } + 3 x + 6$
E)none of these

Question

Find a polynomial with the given zeros.  $0,0,0 , \sqrt { 3 } , - \sqrt { 3 }$  
A) $x ^ { 5 } - 3 x ^ { 3 }$
B) $x ^ { 5 } - 6 x ^ { 3 }$
C) $x ^ { 5 } - x ^ { 3 } + 3$
D) $x ^ { 2 } + 3 x + 6$
E)none of these

Quizplus · Accepted Answer

Given zeros can be used to form the polynomial by multiplying the factors corresponding to each zero. For $0, 0, 0$, the factors are $x, x, x$ or $x^3$. For $\sqrt{3}$ and $-\sqrt{3}$, the factors are $x - \sqrt{3}$ and $x + \sqrt{3}$, which multiply to $x^2 - 3$. Multiplying $x^3$ and $x^2 - 3$ gives $x^5 - 3x^3$.

Find a Polynomial with the Given Zeros 0,0,0,3,−30,0,0 , \sqrt { 3 } , - \sqrt { 3 }0,0,0,3​,−3​

Find a Polynomial with the Given Zeros $0,0,0 , \sqrt { 3 } , - \sqrt { 3 }$