Question

Find α , β are the zeros of polynomial α + β =6 and αβ = 4 then write the polynomial.

Answer 1

α + β =6 =>α = 6 - β
αβ = 4
=>(6-β)(β) =4
=>6β - β² =4
=>β² = 6β - 4
=>β²+4 = 6β
=>(β²+4+4β)=10β
=>(β+2)²=10β

Polynomial:
f(x) = x²-(α+β)x+(αβ)
= x²-6x+4.

Answer 2

α + β =6 =>α = 6 - β

αβ = 4

=>(6-β)(β) =4

=>6β - β² =4

=>β² = 6β - 4

=>β²+4 = 6β

=>(β²+4+4β)=10β

=>(β+2)²=10β

Polynomial:

f(x) = x²-(α+β)x+(αβ)

= x²-6x+4.