Explain whether or not the plant labeled p(x)=x2+x+3 has any rational or irrational roots.

frational roots are those numbers that can be written in form where a and b are integers (integers are like -5,-4,-3,-2,-1,0,1,2,3,4, etc)

some examples are 1=1/1, 2=2/2, -4=-4/1, 4/3, 0.111111111111=1/9, etc

irrational numbers are numbers that can't be written that way like pi

numbers that involve √-1 or a square root of any negative number are called complex numbers and are neither rational nor irrational.

roots are the values of x that makes the function equal to 0

set equal to 0

I can't factor so use quadratic formula

for

so

√-11 is a square root of a negative number so it is a complex number. therefore, the function does not have rational or irrational roots

p(x) has no rational or irrational roots

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