Find all the zeroes of the polynomial p(x) = x4 – 7x³ + 9x² + 13x – 4, if two of its zeroes are (2 +√ 3) and ( 2 - √ 3).

All the zeroes of the polynomial p(x) are:

We are given a polynomial expression p(x) as:

Also two of the zeros of the polynomial are:

i.e. the polynomial could be factored as follows:

where q(x) is a polynomial of degree 2

i.e.

i.e.

Hence, we get the value of q(x) as:

Hence, our polynomial could be represented in terms of linear factors as:

i.e. the other two zeros are: -1 and 4

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet