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Let $r$ and $s$ be the roots of $y^2 - 19y + 7$. Find $(r-2)(s-2)$.

 Jun 15, 2019
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y^2 - 19y + 7                      (r - 2) (s - 2)  =  rs - 2s - 2r + 4  =  rs -2(r + s) + 4

 

Using Vieta's Theorem

The sum of the roots , (r + s)  = 19

The product of the roots, rs  = 7

 

So  

 

(r - 2) (s - 2)  =  rs - 2(r + s) + 4  =    7 - 2(19) + 4   =    -27

 

 

cool cool cool

 Jun 15, 2019

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