If α and β be the zeroes of the polynomial ax² + bx + c, find the values of

(i)

(ii)

(ii)

Let the quadratic poynomial be ax² + bx + c , and its zeroes be α and β.

We have

α + β = and α β =

(i)

We have to find the value of

Now, if we recall the identity

(a + b)² = a² + b² + 2ab

Using the identity, we get

{from eqⁿ (1) & (2)}

(ii)

Let’s take the LCM first then we get,

{}

(iii)

Now, recall the identity

(a + b)³ = a³ + b³ + 3a² b + 3ab²

Using the identity, we get

⇒(α + β)³ = α³ + β³ + 3α² β + 3αβ²