Given:
x2 – 5x + k
The co-efficients are a = 1, b = -5 and c = k.
∴ α + β = \(\frac{-b}a\)
⇒ α + β = \(\frac{(-5)}1\)
⇒ α + β = 5 ….(1)
Also, α – β = 1 …..(2)
From (1) and (2), we get:
2α = 6
⇒ α = 3
Putting the value of α in (1), we get β = 2.
Now, αβ = \(\frac{c}a\)
⇒ 3 × 2 = \(\frac{k}1\)
∴ k = 6