Question

find cubic equation whose roots are 1,2,3

Answer 1

let,

α, β and Δ are the roots

⇒ α = 1 ,β = 2 and Δ = 3

general form of cubic equation with roots α, β, and Δ is x³ -x²(α+β+Δ) +x (αβ+βΔ+αΔ)-αβΔ = 0

substituting these values,

x³ -x²(1+2+3)+x [ (1×2) +(2×3) +(1×3) ] -(1×2×3) = 0

x³ - x²(6)+(2+6+3)x-6 =0

x³-6x²+11x-6=0 is the cubic equation with roots 1,2 and 3

Answer 2

for a cubic equation Ax^3+Bx^2+ Cx +D=0
sum of roots = -B/A
sum of roots taken two at a time i.e- 2.1+2.3+3.1= C/A 
product of roots = -D/A
 use this to find the equation