Question

If alpha and beta are the zeros of polynomial p (x) = ax2 +bx+c Then find 1/alpha ^2

Answer 1

If α and β are the zeroes of polynomial ax²+bx+c,

We can say,

α+β=-b/a---------(i)

And,

αβ=c/a

⇒β=c/aα----------(ii)

Putting the value of β in (i) from (ii),

α+c/aα=-b/a

⇒(a²α+c)aα=-b/a

⇒(a²α+c)α=-b

⇒a²α+c=-αb

⇒a²α+αb=-c

⇒α(a²+b)=-c

⇒α=-c/(a²+b)   (Ans.)