Find a fourth degree polynomial equation with integer coefficients that has the given numbers as roots. be sure to show all of your work. 2i, 4-i

Step-by-step explanation:

We are given that the roots of the polynomial are 2i and 4-i.

Since, the given roots are complex roots and we know that, 'Complex roots always occurs in pairs'.

So, we get that,

The roots of the given polynomial are 2i, -2i, 4-i and 4+i.

i.e.

i.e.

i.e.

i.e.

i.e.

i.e.

i.e.

Hence, the fourth degree polynomial having roots 2i, 4-i is .

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.