If alpha and beta are the zeroes of the polynomial x2 - 3x + k, such that alpha-beta = 1, find the value of k.

Answer: k = 2

The given quadratic polynomial is ; x² – 3x + k

The value of

a = 1

b = -3

c = k

also given

α – ß = 1 …………(1)

Let us calculate the sum of the zeros

α + ß = -b/a

α + ß = -(-3)/1

α + ß = 3 ……………………(2)

Let us calculate the products of the zeros

α × ß = c/a

α × ß = c/a

α × ß = k/-3……………………(3)

We know that

(x + y)² – (x – y)² = 4xy

(α + ß)² – (α – ß)² = 4αß

3² – 1² = 4k

4k = 9 – 1

4k = 9 – 1

4k = 8

k = 8/4

k = 2

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