Question

Find the quadric polynomial .
for the zeroes of
$\alpha \beta$

given in each case 2,-1 ​

Answer 1

The minimal quadratic polynomial with roots 2 & –1 is

x²–(2–1)x +(2)(–1)

ie., f(x) = x²–x–2

and the family of such quadratic functions is given by :

p(x) ≡ k(x²–x–2)

where, k ∈ ℝ : k≠0