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The roots of \(7x^2 + x - 5 = 0\) are a and b. Compute \((a - 4)(b - 4)\).

 Jan 24, 2021
 #1
avatar+116126 
+1

By Vieta's Theorem

 

a +  b =   -1/7   ⇒   -4a   -4b =  4/7

ab  = -5/7

 

So

 

(a - 4) ( b  - 4)   =  

 

ab   + (- 4a - 4b )   +  16   =

 

-5/7   + 4/7   + 16   =

 

-1/7  +  16   =

 

111/7     (  CORRECTED  )

 

 

cool cool cool

 Jan 24, 2021
edited by CPhill  Jan 24, 2021
 #2
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-1

hmm, incorrect.frown

Guest Jan 24, 2021
 #3
avatar+116126 
0

OOPS....small error....now corrected  !!!

 

 

cool cool cool

CPhill  Jan 24, 2021
 #4
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0

Correct!

Guest Jan 24, 2021

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