+184 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.
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.
+184 It's not my homework though, my real hw is so easy I wouldn't bother putting it here.
+184 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.
+184 Anyways I figured it out, the answer is 23/4 for anyone wondering what it is.
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.
+184 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.
+184 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
