Write a polynomial f (x) that meets the given conditions.
-Polynomial of lowest degree with zeros of $\frac { 3 } { 4 }$ (multiplicity 2 ) and $\frac { 1 } { 3 }$ (multiplicity 1 ) and with $f ( 0 ) = - 18$
A) $f ( x ) = 96 x ^ { 3 } - 176 x ^ { 2 } + 102 x - 18$
B) $f ( x ) = 48 x ^ { 3 } - 88 x ^ { 2 } + 51 x - 18$
C) $f ( x ) = 96 x ^ { 3 } - 176 x ^ { 2 } - 6 x - 18$
D) $f ( x ) = 48 x ^ { 3 } - 88 x ^ { 2 } + 3 x - 18$

Question

Quizplus · Accepted Answer

The polynomial is $f ( x ) = ( x - \frac { 3 } { 4 } ) ^ { 2 } ( x - \frac { 1 } { 3 } ) ( x ) + c$. Since $f ( 0 ) = - 18$, we have $- \frac { 3 } { 4 } \cdot \frac { 1 } { 3 } \cdot 0 + c = - 18$, so $c = - 18$. Therefore, $f ( x ) = ( x - \frac { 3 } { 4 } ) ^ { 2 } ( x - \frac { 1 } { 3 } ) ( x ) - 18 = 96 x ^ { 3 } - 176 x ^ { 2 } + 102 x - 18$.

Write a Polynomial F (X) That Meets the Given Conditions 34\frac { 3 } { 4 }43​

Write a Polynomial F (X) That Meets the Given Conditions $\frac { 3 } { 4 }$