Question 1051365: Find all solutions to the equation.
x^3+x^2-14x-24=0
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website! .
Find all solutions to the equation.
x^3+x^2-14x-24=0
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Since the coefficients of the equation are integer numbers and since the leading coefficient is 1,
the rational solutions (if they exist) must be integer numbers among the divisors of the constant term.
So, you need to check for zeroes all integer divisors of the constant term 24:
1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 24, -24.
I did it using Excel in my computer.
x f(x)
1 -36
-1 -10
2 -40
-2 0
3 -30
-3 0
4 0
-4 -16
6 144
-6 -120
8 440
-8 -360
12 1680
-12 -1440
24 14040
-24 -12936
The zeroes are -3, -2, 4.
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