Q) If α, β are the zeroes of the polynomial p(x) = x^2 − 3x − 1, then find the value of 1/α +1/β.

(Q21 – 30/1/1 – CBSE 2026 Question Paper)

Ans:        

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

For p (x) = 0, x ² – 3 x – 1 = 0

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

a x ² + b x + c

here, we get, a = 1, b = – 3 and c = – 1

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

Sum of the zeroes, α + β = = 3

and Product of zeroes, α . β = = – 1

Step 3: ∵ We need to find value of 

Let’s simplify it:

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

∴

=   = – 3

Therefore, the value of is – 3. 

Please press the “Heart” button if you like the solution.