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

Answer 1

(r-2)(s-2)
= rs - 2s - 2r + 4
= rs - 2(s+r) + 4

but for y^2 - 19y + 7 , the sum of the roots = 19 and the product of the roots = 7

so ....
rs - 2(s+r) + 4
= 7 - (19) + 4
= -8