SOLUTION: Find all solutions to the equation. x^3+x^2-14x-24=0

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
~~~~~~~~~~~~~~~~~~~~~~

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.

RELATED QUESTIONS
find all roots of the equation:... (answered by stanbon)

x^2+14x+40=0 find all... (answered by jim_thompson5910)

Find all real solutions to the equation 4^x - 5(2^x) - 24 =... (answered by Alan3354)

Which solutions all apply to... (answered by Fombitz)

find all real solutions. Do not use a calculator. x^3+5x^2-14x= 0 (answered by stanbon)

"Find the zeros of the polynomial equation X^4 + 2X^3 - 13X^2 - 14X + 24 =... (answered by MathLover1,greenestamps)

Find all solutions of the equation |x^2 - 14x + 29| =... (answered by ikleyn,Boreal)

I need to find all the imaginary solutions of the equation by factoring. x^4+14x^2-32=0 (answered by richard1234)

Find all solutions of the equation |x^2 - 14x + 29| = 4. Discuss whether or not your... (answered by josgarithmetic)