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

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Question 1076467: Let r and s be the roots of y^2 - 19y + 7. Find (r-2)(s-2).
Found 2 solutions by rothauserc, MathTherapy:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
y^2 -19y + 7 = 0
:
complete the square
:
y^2 -19y +(361/4) = -(28/4) +(361/4)
:
(y -19/2)^2 = 333/4
:
y = (19/2) +(square root(333)/2) = (37.2463/2) = 18.6231
:
y = (19/2) -(square root(333)/2) = (.7537/2) = .3768
:
let r = 18.6231 and s = .3768
:
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(r-2)(s-2) = (18.6231-2)(.3768-2) = −26.9826
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:

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Let r and s be the roots of y^2 - 19y + 7. Find (r-2)(s-2).
(r – 2)(s – 2)_____rs – 2r – 2s + 4______rs – 2(r + s) + 4

Product, or rs+=+c%2Fa+=+7%2F1+=+7

Sum, or r+%2B+s+=+-+b%2Fa+=+-+-+19%2F1+=+19



rs – 2(r + s) + 4

7 – 2(19) + 4 -------- Substituting 7 for rs, and 19 for r + s



It's as simple as that! No complex calculations are necessary!