Question

If α, β are the roots of the equation ax² + bx + c = 0, then the roots of the equation ax² + bx(x+1) + c(x+1)² = 0 are:

• A. α-1, β-1
• B. α+1, β+1
• C. (α)/(α-1), (β)/(β-1)
• D. (α)/(1-α), (β)/(1-β)

Hint:

Try variable transformation when expressions repeat.

Answer 1

The Correct Option is D

Step 1: Substitute y = (x)/(x+1). Transform the equation accordingly.
Step 2: Root relation. New roots become: (α)/(1-α), (β)/(1-β)