The graph of the line y = 3x + a intersects the graph of the parabola y = in two points. If the distance between these points is 3√30, what is the value of a

? Express your answer as a common fraction.

HumenBeing Jul 19, 2023

#1**0 **

The two points of intersection are (x,3x+a) and (x,x2+x). Setting these equal, we get [3x+a=x^2+x.]Then x2−2x−a=0. By the quadratic formula, the roots of this equation are [x=\frac{2 \pm \sqrt{5}}{2}.]Since the distance between the two points is 3√30, the two roots must be (2 - sqrt(5)/2 and (2 + sqrt(5))/2.

The sum of the roots is 2/2=1, so a=−1+5/2=3/2.

Guest Jul 19, 2023

#3**0 **

It's not my homework though, my real hw is so easy I wouldn't bother putting it here.

HumenBeing Jul 19, 2023

#6**0 **

Not every question that isn't anywhere else on the internet is from your homework... In fact, homework problems might be more likely to be on the internet.

HumenBeing Jul 19, 2023

#7**+1 **

Anyways I figured it out, the answer is 23/4 for anyone wondering what it is.

HumenBeing Jul 19, 2023

#8**0 **

Good job! Next time before you run to this website for answers to your homework, think: do I really need some egotistic retired professor to solve it for me, or can my 1 iq figure it out? Also, most homework problems (like a o p s) are not publicly available, or would be if cheaters like you didn't post them here.

Guest Jul 19, 2023

#9**0 **

Most cheated questions are posted in LaTeX, otherwise they might not be cheated questions. And I didn't figure out the answer myself anyways, my friend helped me.

HumenBeing Jul 19, 2023

#11**0 **

I didn't know, but someone else said it on a previous question here (plus people started randomly insulting each other) :https://web2.0calc.com/questions/what-is-the-number-of-units-in-the-length-of-overline-ab

HumenBeing
Jul 19, 2023