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Let $a$ and $b$ be the roots of the quadratic $x^2 - 5x + 3 = 2x^2 + 14x + 8.$ Find the quadratic whose roots are 1/(a + 1) and 1/(b + 1).

 May 5, 2024
 #1
avatar+128796 
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Rearrange as

 

x^2 +19x + 5  =  0

 

By Vieta  .....

a + b  =  - 19

ab  = 5

 

1/ ( a + 1)  +  1 / (b + 1)  =  

 

[ (a + b) + 2 ] /  [ ab + (a + b) + 1 ]   =

 

[ -19 + 2 ] / [ 5 - 19 + 1 ]  =

 

-17  /  - 13  = 

 

17  /  13

 

 

cool cool cool

 May 5, 2024

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