Question

Alpha and beta are the roots of the equation lx2-mx+n=0,find the equation whose roots are alpha/beta and beta/alpha.

Answer 1

ℓϰ²-мϰ+η=0
α and β are the roots of the lx²-mx +n=0
α+β=-(-m/l)=m/l
αβ=n/l
let S and P be the sum of the roots of zeros and product of the zeros of the required equation
s=α/β+β/α
=α²+β²/αβ
=(α+β)²-2αβ
=(m/l)²-2n/l
=m²/l²-2n/l
=m²-2nl/l²
P=αβ
=n/l
the required equation=x²-sx+p=0
=x²-(m²-2nl/l²)x+n/l