Find a polynomial with the given zeros. $1,3,6$
A) $\quad 10 x ^ { 2 } + 27 x - 18$
B) $\quad x ^ { 3 } - 10 x ^ { 2 } + 27 x - 18$
C) $\quad 27 x ^ { 3 } - 10 x ^ { 2 } + 27 x - 18$
D) $\quad x ^ { 3 } + 10 x ^ { 2 } - 27 x + 18$
E) none of these

Question

Quizplus · Accepted Answer

A polynomial with zeros $1, 3, 6$ can be found by using the fact that if $r$ is a root, then $(x-r)$ is a factor of the polynomial. Thus, the polynomial can be written as $(x-1)(x-3)(x-6)$. Expanding this product gives $x^3 - 10x^2 + 27x - 18$, which matches option B.

Find a Polynomial with the Given Zeros 1,3,61,3,61,3,6 A) 10x2+27x−18\quad 10 x ^ { 2 } + 27 x - 1810x2+27x−18

Find a Polynomial with the Given Zeros $1,3,6$ A) $\quad 10 x ^ { 2 } + 27 x - 18$