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The roots of the quadratic \(x^2+8x+4\) are the same as the roots of the quadratic \(Ax^2+Bx+1\). What is \(A+B\)?

 Apr 2, 2020
 #1
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I recommend using the Quadratic Equation. I'm too lazy I'm gonna go play some video games bye see you guys in a few hours!

 Apr 2, 2020
 #2
avatar+111321 
+1

By Vieta :

 

Sum of  roots  of  first  quadratic  =  -8/1  =  -8

Product of the roots  of  1st  quadratic = 4/1   =4

 

This implies, that, in the  second quadratic

 

-8 = -B/ A   ⇒   8  = B /A   ⇒  8A  = B        (1)

And

1 / A  =   4     ⇒  A  = 1/4         (2)

 

Sub  (2)  into (1)   and  we have  that

 

8 (1/4)  = B   =   2

 

So

 

A + B   =    (1/4)  +  2  =    9 / 4

 

 

 

cool cool cool

 Apr 2, 2020

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