Prove that the equation 12x2+70x+a2+1=0 for any value of a does not have any positive roots. I need help ASAP! Please someone Help

The solution follows below

Step-by-step explanation:

12·x²+70·x+a²+1=0

Let's find the discriminant

D=4900-12*4*(a²+1)=4900-48(a²+1) <4900 for any a

So √D<70    (1) for any a

first root X1= (-70-√D)/24<0  so -70-√D<0

second root x2=(-70+√D)/24<0  so -70+√D<0  (√D<70 look to inequality (1))

=> Both roots are negative for any a.

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

answer: what is the conflict?

step-by-step explanation:

*what has happened to new york city?

*what is in the time capsule?

* what did the kidz see that gave them hope?

*what will they do with what they find?

* how will they save the city?

* what challenges will they face along the way?

*what big choice will they make at the climax of the story?

* what lesson do they learn at the end of the story?