Find a cubic function with the given zeros.
-$4 , - 2,5$
A) $f ( x ) = x ^ { 3 } - 7 x ^ { 2 } + 2 x - 40$
B) $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } + 2 + 40$
C) $f ( x ) = x ^ { 3 } - 7 x ^ { 2 } + 2 x + 40$
D) $f ( x ) = x ^ { 3 } - 7 x ^ { 2 } - 2 x + 40$

Question

Quizplus · Accepted Answer

The correct answer is C because the zeros of a cubic function are the values of x that make the function equal to zero. To find the cubic function with the given zeros, we can use the following formula:$$f(x) = (x - z_1)(x - z_2)(x - z_3)$$where $z_1, z_2, z_3$ are the zeros of the function.Substituting the given zeros into the formula, we get:$$f(x) = (x - 4)(x + 2)(x - 5)$$Expanding the product, we get:$$f(x) = x^3 - 7x^2 + 2x + 40$$Therefore, the correct answer is C.

Find a Cubic Function with the Given Zeros 4,−2,54 , - 2,54,−2,5

Find a Cubic Function with the Given Zeros $4 , - 2,5$