Q) α, β are zeroes of the polynomial p(x) = 3 x ² − 6x − 5. Find the value of 1/α ² + 1/β ².

(Q 24 – 30/4/2 – CBSE 2026 Question Paper)

Ans:

Step 1: Given polynomial, p (x) = 3 x ² – 6 x – 5

For p (x) = 0, 3 x ² – 6 x – 5 = 0

Let’s compare the given polynomial with standard quadratic polynomial:

a x ² + b x + c

here, we get, a = 3, b = – 6 and c = – 5

Step 2: Next, we know that if α and β are zeroes of quadratic polynomial, then

Sum of the zeroes, α + β = – = – = 2

and Product of zeroes, α . β =

Step 3: ∵ We need to find value of

Let’s simplify it:

∵ by algebraic identity, (a + b) ² = a ² + b ² + 2 ab

∴ a ² + b ² = (a + b) ² – 2 a b

∴ α ² + β ² = (α + β) ² – 2 α β

By substituting this in our expression we get:

 =

Step 4: Now we substitute the value of (α + β) and α . β from step 2

∴  

=  =

= = 2.64

Therefore, the value of is 2.64.

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