Q)  If 𝛼, β are zeroes of quadratic polynomial x² + x – 2, find the value of

Ans: In the given polynomial equation f(x), to find zeroes, we will start with f(x) = 0

Therefore, x² + x – 2 = 0

Step 1: Given that the roots of the polynomial are α and β.

We know that sum of roots (α + β) = 

∴    α + β =  = – 1 …………(i)

Next, we know that the product of the roots (α x β) =

∴  α . β =   = – 2 ………… (ii)

Step 2: Next, we need to find the value of

Let’s solve this to simplify:

= ………(iii)

We know that (a + b)² = a² + b² + 2 a b

or we can say that a² + b² = (a + b)² – 2 a b

Therefore, α² + β² = (α + β)² – 2 α β

Transferring this value in equation (iii), we get:

=

Step 3: Next, we transfer values of (α + β) and α β from equations (i) and (ii)

=

=

=

=

Therefore, the value of is –

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