SOLUTION: Find a polynomial of degree 3 with real coefficients and zeros of ​-3,-​1, and​ 4, for which f(-2)=-30. f(x)=

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find a polynomial of degree 3 with real coefficients and zeros of ​-3,-​1, and​ 4, for which f(-2)=-30. f(x)=      Log On


   

Question 1198420: Find a polynomial of degree 3 with real coefficients and zeros of ​-3,-​1, and​ 4, for which f(-2)=-30.
f(x)=
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Find a polynomial of
degree 3+
zeros of :
x%5B1%5D=-3
x%5B2%5D=-1
​ x%5B3%5D=4
for which f%28-2%29=-30

f%28x%29=a%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29
f%28x%29=a%28x-%28-3%29%29%28x-%28-1%29%29%28x-4%29
f%28x%29=a%28x%2B3%29%28x%2B1%29%28x-4%29
f%28x%29=a%28x%5E3+-+13x+-+12%29........if f%28-2%29=-30, we have

-30=a%28%28-2%29%5E3+-+13%28-2%29++-+12%29
-30=a%286%29
a=-30%2F6
a=-5

and your polynomial is

f%28x%29=-5%28x%5E3+-+13x+-+12%29
f%28x%29=-5x%5E3+%2B+65x+%2B+60