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alpha and beta are roots of ax2+bx+c then the equation ax2-bx(x-1)+c(x-1)2 has roots?
11 months ago

ax2-bx(x-1)+c(x-1)2=0
divide by (x-1)^2
a(x/(x-1))^2-bx/(x-1)+c=0
now set x/(x-1)= – y
so eqn becomes
ay^2+by+c=0
roots of this eqn are obviously alpha and beta
since  x/(x-1)= – y
therefore x= y/(y+1)
so roots of ax2-bx(x-1)+c(x-1)2=0 are alpha/(alpha+1) and beta/(beta+1)
11 months ago
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