Find a polynomial with the given zeros. $- 1,5 , - \sqrt { 7 } , \sqrt { 7 }$
A) $x ^ { 5 } - 4 x ^ { 4 } - 12 x ^ { 3 } + 28 x ^ { 2 } + 35 x - 2$
B) $x ^ { 4 } - 12 x ^ { 2 } + 35$
C) $x ^ { 4 } - 12 x ^ { 3 } - 4 x ^ { 2 } - 28 x + 35$
D) $x ^ { 4 } - 4 x ^ { 3 } - 12 x ^ { 2 } + 28 x + 35$
E)none of these

Question

Find a polynomial with the given zeros.   $- 1,5 , - \sqrt { 7 } , \sqrt { 7 }$  
A) $x ^ { 5 } - 4 x ^ { 4 } - 12 x ^ { 3 } + 28 x ^ { 2 } + 35 x - 2$
B) $x ^ { 4 } - 12 x ^ { 2 } + 35$
C) $x ^ { 4 } - 12 x ^ { 3 } - 4 x ^ { 2 } - 28 x + 35$
D) $x ^ { 4 } - 4 x ^ { 3 } - 12 x ^ { 2 } + 28 x + 35$
E)none of these

Quizplus · Accepted Answer

The polynomial with the given zeros $-1, 5, -\sqrt{7}, \sqrt{7}$ is formed by multiplying the factors $(x + 1)(x - 5)(x + \sqrt{7})(x - \sqrt{7})$. This simplifies to $x^4 - 4x^3 - 12x^2 + 28x + 35$.

Find a Polynomial with the Given Zeros −1,5,−7,7- 1,5 , - \sqrt { 7 } , \sqrt { 7 }−1,5,−7​,7​

Find a Polynomial with the Given Zeros $- 1,5 , - \sqrt { 7 } , \sqrt { 7 }$