Question

If alpha and beta are the zeroes of the quadratic polynomial

ax^{​​​​2}+bx+c, find a quadratic polynomial whose zeroes are 1/alpha and 1/beta

Answer 1

Ax² + bx +c =0
zeroes α,β

sum of roots = α+β = -b/a
products of roots = αβ = c/a

For quadratic equation with roots 1/alpha and 1/beta

1/α+1/β=-b/a
(α+β)/αβ=-(b/a)
(-b/a)/(c/a)=-b/a
-b/c=-b/a
b/c=b/a
And
1/α*1/β=c/a
1/αβ=c/a
So αβ=a/c

So the quadratic equation is cx^2+bx+a