Question

If alpha, beta are the zeroes of x2-2x+3, find a quadratic equation whose roots are (alpha-1)(beta+1), (beta-1)(beta+1)

Answer 1

since the roots of the quadratic are 1±√2 i

(alpha-1) and (beta-1) are ±√2 i

If you want real coefficients, this will not produce the required complex conjugates.

I suspect a typo. So, fix that and then just plug and chug.