Question

If alpha and beta be the zeroes of the quadratic polynomial x²+ax+b,evaluate
(I) 1/alpha+1/beta
(2) alpha ²/beta + beta²/alpha

Answer 1

i hope this will help you

Answer 2

x²+ax+b

Here a=1, b=a, c=b

(i)So, α+β = -b/a
or α+β= -a/1 = -a
. αβ = c/a
or αβ = b/1 = b

1/α+1/β = β+α/αβ
. = -a/b (answer)
That is the right solution for (¡)

(ii)α²/β + β²/α = α³+β³/αβ .......(1)

We know that (α+β)³=α³+β³+3αβ(α+β)
So, (-a)³= α³+β³+3(b)(-a)
-a³ +3ab =α³+β³
α³+β³= -a³+3ab

So eq. (1) becomes
-a³+3ab/b (answer)
Which is the correct solution for (ii)

I know it's a bit difficult to understand but you can.