SOLUTION: f(x)=x^3-5x^2-14x f(x)=x^3+4x^2+9x+36 f(x)=x^4+x^3-2x^2+4x-24

Algebra ->  Rational-functions -> SOLUTION: f(x)=x^3-5x^2-14x f(x)=x^3+4x^2+9x+36 f(x)=x^4+x^3-2x^2+4x-24      Log On


   

Question 133347: f(x)=x^3-5x^2-14x
f(x)=x^3+4x^2+9x+36
f(x)=x^4+x^3-2x^2+4x-24
Found 2 solutions by jim_thompson5910, vleith:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Do you want to find the zeros? If so, I'll do the first two for you


x%5E3-5x%5E2-14x=0 Start with the given equation


x%28x%5E2-5x-14%29=0 Factor out the common term "x"


x%28x-7%29%28x%2B2%29=0 Factor the inner expression (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x=0, x-7=0 or x%2B2=0

x=0, x=7 or x=-2 Now solve for x in each case


So our answer is
x=0, x=7 or x=-2


Notice if we graph y=x%5E3-5x%5E2-14x we can see that the roots are x=0, x=7 and x=-2. So this visually verifies our answer.


+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C0%2C+x%5E3-5x%5E2-14x%29+





# 2


x%5E3%2B4x%5E2%2B9x%2B36=0 Start with the given equation

%28x%5E3%2B4x%5E2%29%2B%289x%2B36%29=0 Group like terms


x%5E2%28x%2B4%29%2B9%28x%2B4%29=0 Factor out the GCF x%5E2 out of the first group. Factor out the GCF 9 out of the second group


%28x%5E2%2B9%29%28x%2B4%29=0 Since we have the common term x%2B4, we can combine like terms




Now set each factor equal to zero:

x%5E2%2B9=0 or x%2B4=0

Now solve for x for each factor:

x=0%2B-sqrt%28-9%29 or x=-4


x=3i, x=-3i or x=-4


So our solutions are

x=-4, x=3i or x=-3i

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Given: f%28x%29=x%5E3-5x%5E2-14x
f%28x%29=+%28x%29%28x%5E2-5x-14%29+
f%28x%29+=+%28x%29%28x-7%29%28x%2B2%29+
Given: f%28x%29=x%5E3%2B4x%5E2%2B9x%2B36
f%28x%29=%28x%5E2%29%28x%2B4%29+%2B%289%29%28x%2B4%29
f%28x%29=%28x%5E2+%2B+9%29%28x%2B4%29

Given: f%28x%29=x%5E4%2Bx%5E3-2x%5E2%2B4x-24
f%28x%29=x%5E4%2Bx%5E3-2x%5E2%2B4x-24
f%28x%29=x%5E4-2x%5E2-24+%2Bx%5E3+%2B4x
f%28x%29=%28x%5E4-2x%5E2-24%29+%2B+%28x%5E3+%2B4x%29
f%28x%29=%28x%5E2-6%29%28x%5E2%2B4%29+%2B+x%28x%5E2+%2B4%29
f%28x%29=%28%28x%5E2-6%29%2Bx%29%28x%5E2%2B4%29
f%28x%29=+%28x%5E2%2Bx-6%29%28x%5E2%2B4%29
f%28x%29=+%28x-3%29%28x%2B2%29%28x%2B2%29%28x-2%29
f%28x%29=+%28x-3%29%28x%2B2%29%5E2+%28x-2%29