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The teacher has written an equation of the form  on the board, where  is a quadratic, 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 4.''

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 23, 2020
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Let's say the unknown coefficient of the linear term is  b , so the quadratic expression is:

 

4x2  +  bx  -  24

 

And we want to know what  b  is.

 

Since we know that one of the roots is  4,  we know that if we plug in  4  for  x  into the expression, it will equal  0

So we can make the following equation:

 

4(4)2  +  b(4)  -  24  =  0

 

Can you solve the above equation for  b  ?

 Dec 23, 2020

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