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Problem:

The quadratic \( x^2+7x+20\) has the same roots as the quadratic \( Ax^2+Bx+1\). What is \(A+B\)?

 Dec 28, 2017
 #1
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x^2  + 7x  +  20  =  0

 

The sum of the roots  =  -7/1  =  -7

The product of the roots is  20/1  = 20

 

So.....this implies that in  Ax^2 + Bx + 1  = 0

 

-B/A  =  -7    ⇒  B/A  = 7 ⇒  B =  7A

And

1/A  = 20  ⇒  A =  1/20

So..... B  = 7(1/20)  = 7/20

 

So.....  A + B   =    1/20  + 7/20  =  8/20   =  2/5

 

 

cool cool cool

 Dec 28, 2017

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