Can You Pass Harvard's Entrance Exam?

Entrance examination. If you're reading this ❤️.

What do you think about this problem?

Hello My Friend ! Welcome to my channel. I really appreciate it!
@higher_mathematics

#maths #math

[prithvichidri]

For the guys who directly substituted x= -2🤙

[markjones]

The correct answer is: My parent’s just donated $5M to the school.

[ConceivedSorrow]

I solved it this way:
x³-x² = 12
Extract common factor
x²(1-x) = 12
12 can be written like 2²•3 (prime factorization) so:
x²(1-x) = 2²•3
And comparte the factors:
x² = 2²
1-x = 3 <---> x= -2

[divermike]

Oh ! He didn't calculate the Complex root! That's not the Harvard Way! The roots are X=-2, X= (3 +sqrt (15) i) / 2, X=(3-sqrt(15) i) /2

[wolfhard]

Brings me back to Highschool, when the math teacher filled the blackboard with lots of mystery and lacks of explanation skills, so we understood nothing

[daniellemb]

I am very bad at maths, and had always been.
I watched at x² - x³ = 12 and thought "x has to be negative, let's try with -2", so I calculated mentally and wrote 4+8=12. Seemed good ! So x= -2
Don't ask for the demonstration ! 😃

[tom-kzpb]

Seeing -2 only took about 2 seconds. For Harvard, you should need to find the complex solution, as well.

[celestine]

Different approach: a bit trial and error gives x=-2 as a solution. So dividing the whole equation -x^3 + x^2 -12 = 0 by x + 2 gives -x^2 + 3x - 6 = 0. Which is quadratic, and thus solvable -> but has only imaginairy solutions. I think doing it this way is easier than the method used in the movie.

[jbourdette]

The choice of 8 and 4 looks like magic. Be more formal using Gauss theorem about integer roots and soon get -2, the rest is easy, e.g. use Ruffini and Bhaskara.

[ericr]

I worked out before I saw the youtube, on the right hand side of the screen, first of all X would have to be a negative number, so lets try X = -2, -2 squared is 4, -2 cubed is -8 take 4 - - 8 = 4+8 = 12, of course it is good to watch the youtube in case X is not so obvious.

[niravelniflheim]

Thanks to those explaining that there are 3 answers to find and various methods to get to the complex ones. -2 was always the easy part.

[DoubleplusUngoodthinkful]

This is the first time I have ever seen the letter "X" drawn as back-to-back Cs.

[lefantomer]

If you can't and you still want to go to Harvard, go over to the Admissions Office and plunk down a few thou$and -- much much less than for admission to the college as a full daytime live-in student -- and sign up for Extension School. That's the night school. Pick your concentration if you want a degree. You will attend classes at night run by full professors (unless they've changed the policy), will have to do class work and term papers and a thesis like everyone else, attend Commencement and get a Harvard degree for a fraction of what you would have had to pay had you been "accepted".

[robertfitzjohn]

I found x = -2 pretty quickly, but as it's a cubic equation it must have three roots.
Surely to get into Harvard you have to do better than just say "oh, the other roots are complex, so I won't bother with them"? (Unless they specifically asked for only real roots, of course.)
After a bit of work I managed to find the complex roots, and substitute them back into the original equation to prove they were correct.
Then again, I did sit the Mathematics entrance exam for Natural Science at Oxford, some decades ago.

[MandyFlame]

Factor directly as (x+2)(x^2-3x+6)=0 (By inspection x=-2 is a solution, then just work out the other bracket)! Then solve the second bracket using the quadratic formula to find the complex roots.

[algorithminc.]

I look forward to checking out your channel. Subscribed. Thanks. Cheers

[ila]

There is no entrance examination for Harvard University.

[The_Mega_AnalistSci]

I just do not know why is he doing that and not doing by Ruffini´s method which is x10 times easier and you get the result faster.

[luciu]

Guess the x=-2
Factor the expresion using polynomes rules
Solve for cases
Way easier

[kumertd]

Gosh, what does higher mathematics mean in 2024..?