Question 1076467
Let r and s be the roots of y^2 - 19y + 7. Find (r-2)(s-2).
<pre>(r – 2)(s – 2)_____rs – 2r – 2s + 4______rs – 2(r + s) + 4
Product, or {{{rs = c/a = 7/1 = 7}}}
Sum, or {{{r + s = - b/a = - - 19/1 = 19}}}

rs – 2(r + s) + 4
7 – 2(19) + 4 -------- Substituting 7 for rs, and 19 for r + s
{{{highlight_green(matrix(1,7,(r - 2)(s - 2), "=", rs - 2(r + s) + 4, "=", 7 - 2(19) + 4, "=", - 27))}}}
It's as simple as that! No complex calculations are necessary!