Question

trying to get crit points of

fx = x+y=0
fy = 76x+240+y^3 = 0

im having a hard time with algebra. i cant get my points to become the ones here:http://www.wolframalpha.com/input/?i=x%2By%3D0%2C+76x%2B240%2By%5E3%3D0

Answer 1

you need to solve :

\(y^3 -76y +240 = 0 \)

right ?

Answer 2

yes just system of equations

Answer 3

its originally
fx = 76x+76y=0
fy = 76x+240+y^3=0

just need to solve of x and y
ive been stuck with this for a while now >.<

Answer 4

yeah,
that gives below simulataneous equations :

x+y = 0
76x + 240 + y^3 = 0

Answer 5

solve for y from equation, and substitute it in second equation
u wud get :

\(y^3 - 76y + 240= 0 \)

Answer 6

you need to pull ur precalculus skills,
heard of 'rational root theorem' before ?

Answer 7

its either i dont know or dont remember lol. ill look it up tho thanks!

Answer 8

here it is :


rational roots of any polynomial will be of form p/q
p = factors of constant term
q = factors of leading coefficient

Answer 9

so simply find factors of 240
and keep testing which one satisfies the given polynomial

Answer 10

once u get lucky,
u can simply divide it to get a quadratic equaiton,
and use quadratic formula to find remaining two zeroes