Question

if α,β are zeroes of a quadratic polynomials 3X²-6x+4,find the value of (α/β+β/α)+2(1/α+1/1/β)+3αβ

Answer 1

Let’s see if I can offer a third answer. Let SS and PP be the sum and product of αα and ββrespectively. Then the described expression is

E=αβ+βα+2(1α+1β)+3αβ=S(S+2)P+3P−2E=αβ+βα+2(1α+1β)+3αβ=S(S+2)P+3P−2

with S=2S=2 and P=43P=43. So,

E=8E=8.