SOLUTION: Given that f(x) is a cubic function with zeros at −6, 0, and 4, find an equation for f(x) given that f(−7)=−8.

Algebra ->  Rational-functions -> SOLUTION: Given that f(x) is a cubic function with zeros at −6, 0, and 4, find an equation for f(x) given that f(−7)=−8.      Log On


   

Question 1188473: Given that f(x) is a cubic function with zeros at −6, 0, and 4, find an equation for f(x) given that f(−7)=−8.
Found 3 solutions by ikleyn, MathLover1, Solver92311:
Answer by ikleyn(52806) About Me  (Show Source):
You can put this solution on YOUR website!
.

First step is to write  f(x) = ax*(x+6)*(x-4),  where "a" is some real number (a leading coefficient).



Second step is to find the value of "a" by substituting x= -7 into the equation.


You get then


    -8 = a*(-7)*(-1)*(-11)

    -8 = -77a

     a = 8%2F77.


THEREFORE, the polynomial is  f(x) = %288%2F77%29%2Ax%2A%28x%2B6%29%2A%28x-4%29.    ANSWER

Solved and explained.



Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


given:
zeros at -6, 0, and 4
f%28-7%29=-8

f%28x%29+=a%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29
f%28x%29+=a%28x-%28-6%29%29%28x-0%29%28x-4%29
f%28x%29+=a%28x%2B6%29%28x%29%28x-4%29
f%28x%29+=a%28x%5E3+%2B+2x%5E2+-+24x%29...........substitute f%28-7%29=-8
-8=a%28%28-7%29%5E3+%2B+2%28-7%29%5E2+-+24%28-7%29%29
-8=a%28-77%29
a=-8%2F%28-77%29
a=8%2F77
f%28x%29+=%288%2F77%29%28x%5E3+%2B+2x%5E2+-+24x%29
f%28x%29+=%288%2F77%29+x%5E3%2B+%2816%2F77%29x%5E2+-+%28192%2F77%29x




Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!
Sunday, April 2, 2017
7:06 PM


A cubic function in has exactly three complex factors of the form , , , where is a zero of the function. The family of functions given by:



The particular function you are looking for is such that



So solve:



For and then find the product of your four known factors and simplify

John

My calculator said it, I believe it, that settles it

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