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Find an equation for a least-degree polynomial that has a double root at 2 and contains (−1, 0) and (1, -3).

 Feb 15, 2021
 #1
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If  this  has a double root  at 2  and (-1,0)  is on the  graph......then it  must  have  AT LEAST  3  zeroes

 

Let's  assume  that  it  is   degree 3   and has  the form :

 

f(x)  = a ( x - 2)^2  ( x + 1)

 

And since  ( 1, -3)  is on the  graph, then  we  have  that

 

-3  = a ( 1 -2)^2  ( 1 + 1)

 

-3   =a ( -1)^  * 2

 

a  = -3/2

 

Then the polynomial   f(x)  =(-3/2) (x -2)^2 ( x + 1)     should  fit the bill

 

See here :  https://www.desmos.com/calculator/1evpqa5v9z

 

 

cool cool cool

 Feb 15, 2021

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