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The teacher has written a quadratic on the board, but Heather can't read the linear term. She can see that the quadratic term is 4x^2 and that the constant is -24. She asks her neighbor, Noel, what the linear term is. Noel decides to tease her and just says, ``One of the roots is 8.'' Heather then says, ``Oh, thanks!'' She then correctly writes down the linear term. What was the linear term? Include entire term, not simply the coefficient

 Dec 30, 2020
 #1
avatar+117546 
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4x^2  +  bx    - 24

 

Since 8 is a  root....performing some  synthetic division

 

8  [  4      b         -24        ]

             32       8b + 256

    ______________________

      4    b + 32       8b  +  232

 

So

 

8b   + 232     =   0

 

8b    =  - 232

 

b  =   -29

 

So

 

4x^2   -  29x   - 24   =    0

 

(4x  + 3) ( x - 8 )  =  0

 

The linear term is   (4x + 3)

 

 

cool cool cool

 Dec 30, 2020
 #2
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One root is 8    So  (x-8) is part....this results in:
(x-8)(4x+3)             = 4x-29x-24

so  4x+3

 Dec 30, 2020

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