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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.

 

 Jul 19, 2023
 #1
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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​​.

 Jul 19, 2023
 #2
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Looks like someone's cheating again!

 Jul 19, 2023
 #3
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It's not my homework though, my real hw is so easy I wouldn't bother putting it here. 

 Jul 19, 2023
 #4
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I sorta agree with you. Just because they gave you a question does not mean that they are a hw cheater. 

history  Jul 19, 2023
 #5
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Sureeeee... It's just a "challenge". That looks suspiciously like a homework problem, that doesn't exist anywhere else on the internet. Definetly not homework!

Guest Jul 19, 2023
 #6
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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.

 Jul 19, 2023
 #7
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Anyways I figured it out, the answer is 23/4 for anyone wondering what it is. 

 Jul 19, 2023
 #8
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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
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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. 

 Jul 19, 2023
 #10
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you seem to know an awful lot about what a cheated question looks like

Guest Jul 19, 2023
 #11
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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

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