I have to create a rational function with the characteristics: 3 real zeros(1 of them of multiplicit

Junaid Ayala

Junaid Ayala

Answered question

2022-02-18

I have to create a rational function with the characteristics: 3 real zeros(1 of them of multiplicity 2). y-intercept 1. vertical asymptote at x=-2 and x=3. oblique asymptote y=2x+1. Ive

Answer & Explanation

poskakatiqzk

poskakatiqzk

Beginner2022-02-19Added 8 answers

You almost did all the work (may be you forgot to add the conditions (a2,a3,b2,b3).
Now, using the formula you proposed, perform the long division to get
y=2(xa)2(xb)(x+2)(x3)=2x(4a+2b2)+O(1x
which makes
4a+2b2=1b=122a
So
y=2(xa)2(x+2a12)(x3)(x+2)
If x=0 then
16(a24a3)=1
The cubic equation in a shows only one real root which is 1.06715.
If you want to look fancy, using the hyperbolic solution to get
a=11216cosh(13cosh1(1295))

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