Question

C(t)=2(t-4)(t+1)(t-6)

Answer 1

Question: find the x- or t intercepts of the polynomial function:

c(t)=2(t-4)(t+1)(t-6)​.

Solution:

the t-intercept (zeros of the function) of the given polynomial function occurs when c (t) = 0, that is when:

`c(t)\text{ = 0 = }2\mleft(t-4\mright)\mleft(t+1\mright)\mleft(t-6\mright)​`

this can only happen when any of the factors of the polynomial are zero:

t-4 = 0, that is when t = 4

t + 1 = 0 , that is when t = -1

and

t-6 = 0, that is when t = 6.

then, we can conclude that the t-intercept (zeros of the function) of the given polynomial are

t = 4, t = -1 and t = 6.