A third-degree polynomial function f has real zeros -2, 1/2, and 3, and its leading coefficient negative. Write an equation for f. Sketch
the graph of f. How many different polynomials functions are
possible for f?

f(x) = -x³ + (3/2)x² + (11/3)x + 3.

Step-by-step explanation:

Given, real zeroes of f(x) are -2, 1/2, 3.

⇒ f(x)  = -(x+2)(x-1/2)(x-3). (- sign because given leading coefficient is negative)

⇒f(x) = -x³ + (3/2)x² + (11/3)x + 3.

as the real zeroes are fixed, only one such polynomial is possible.

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,