Asked by Krystel Mae Elento
find the roots of x3+6x2+11x+6=0 what is the formula and answer how to solve this ??
Answers
Answered by
Reiny
Even though a formula to solve a cubic equation exists, nobody in their right mind would use it
http://www.math.vanderbilt.edu/~schectex/courses/cubic/
The first thing I usually do is to try the factor theorem
look for factors of 6 which might work
try x = ±1, ±2, ±3
on my second try, I found x = -1 to be a root,
so x+1 is a factor
Use either long algebraic division or synthetic division to get the other factor of x^2 + 5x + 6
which factors once more to
(x+2)(x+3)
so ...
x^3+6x^2+11x+6=0
(x+1)(x+2)(x+3) = 0
x = -1, -2, -3
We were lucky for this to happen, if no nice rationals were found, we could use more advanced methods such as Newton's Method
http://www.math.vanderbilt.edu/~schectex/courses/cubic/
The first thing I usually do is to try the factor theorem
look for factors of 6 which might work
try x = ±1, ±2, ±3
on my second try, I found x = -1 to be a root,
so x+1 is a factor
Use either long algebraic division or synthetic division to get the other factor of x^2 + 5x + 6
which factors once more to
(x+2)(x+3)
so ...
x^3+6x^2+11x+6=0
(x+1)(x+2)(x+3) = 0
x = -1, -2, -3
We were lucky for this to happen, if no nice rationals were found, we could use more advanced methods such as Newton's Method
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