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in Polynomials by (32.2k points)
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If α, β are the zeroes of the polynomial f(x) = x2 – 5x + k such that α – β = 1, find the value of k.

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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

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