Find a polynomial with the given zeros. $1,1,7$
A) $9 x ^ { 2 } + 15 x - 7$
B) $x ^ { 3 } + 9 x ^ { 2 } - 15 x + 7$
C) $15 x ^ { 3 } - 9 x ^ { 2 } + 15 x - 7$
D) $x ^ { 3 } - 9 x ^ { 2 } + 15 x - 7$
E)none of these

Question

Find a polynomial with the given zeros.​ $1,1,7$ ​
A) $9 x ^ { 2 } + 15 x - 7$
B) $x ^ { 3 } + 9 x ^ { 2 } - 15 x + 7$
C) $15 x ^ { 3 } - 9 x ^ { 2 } + 15 x - 7$
D) $x ^ { 3 } - 9 x ^ { 2 } + 15 x - 7$
E)none of these

Quizplus · Accepted Answer

To find a polynomial with given zeros $1, 1, 7$, we use the fact that if $r$ is a root, then $(x - r)$ is a factor of the polynomial. Thus, the polynomial can be written as $(x - 1)(x - 1)(x - 7)$. Expanding this gives $x^3 - 9x^2 + 15x - 7$, which matches option D.

Find a Polynomial with the Given Zeros 1,1,71,1,71,1,7 ​ A) 9x2+15x−79 x ^ { 2 } + 15 x - 79x2+15x−7

Find a Polynomial with the Given Zeros $1,1,7$
A) $9 x ^ { 2 } + 15 x - 7$