SOLUTION: Construct a polynomial function with the following properties: third degree, only real coefficients, −1 and 2+i are two of the zeros, y-intercept is −15.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Construct a polynomial function with the following properties: third degree, only real coefficients, −1 and 2+i are two of the zeros, y-intercept is −15.      Log On


   

Question 1198743: Construct a polynomial function with the following properties: third degree, only real coefficients, −1 and 2+i are two of the zeros, y-intercept is −15.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
a%28x%2B1%29%28x-%282%2Bi%29%29%28x-%282-i%29%29=-15
a%28x%2B1%29%28x-2-i%29%28x-2%2Bi%29=-15
a%28x%2B1%29%28%28x-2%29%5E2-1%29=-15
a%28x%2B1%29%28x%5E2-4x%2B4%2B1%29=-15
a%28x%2B1%29%28x%5E2-4x%2B5%29=-15
The multiplication for the polynomial is not yet finished, but letting x=0 allows to find the factor, "a".

Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
.

        The post by @josgarithmetic is totally wrong,
        so I came to bring you a correct solution. 


a%28x%2B1%29%28x-%282%2Bi%29%29%28x-%282-i%29%29 = -15

a%28x%2B1%29%28x-2-i%29%28x-2%2Bi%29 = -15

a%28x%2B1%29%28%28x-2%29%5E2%2B1%29 = -15

a%28x%2B1%29%28x%5E2-4x%2B4%2B1%29 = -15

a%28x%2B1%29%28x%5E2-4x%2B5%29 = -15


To find "a", put x=0 in this equation.  You will get

    5a = -15,  a = -15/5 = -3.


So, the polynomial is  -3(x+1)*(x^2-4x+5).    ANSWER

Solved in full and in correct form.


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He re-wrote his post after seeing my post.