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Let m and n be the roots of 7x^2 + 9x + 21 = 0.  Find (m + 7)(n + 7).

 Dec 5, 2019
 #1
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Using the quadratic formula, we get:

 

m=[ -0.6428571429 +1.608332893 i] + 7 = [6.35714 + 1.60833 i ]
n=[ -0.6428571429 -1.608332893 i ] + 7  =  [6.35714 - 1.60833 i ]

 

 [6.35714 + 1.60833 i ] *  [6.35714 - 1.60833 i ] = ~43

 Dec 5, 2019
 #2
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+1

7x^2  +  9x  +  21  = 0

 

And

 

( m + 7)(n + 7)   =    (mn)^2  + 7 (m + n)   +  49     (1)

 

By Vieta,

 

m + n  = - 9/7         (2)

       

And

mn  = 21/7  = 3   square both sides

(mn)^2  = 9        (3)

 

Sub (2)  and (3)  into  (1)    and we have that

 

(m + 7) ( n +7)   =  (9)  + 7(-9/7)  + 49   =      49

 

 

cool cool cool

 Dec 5, 2019

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