Question

If alfa and beta are the zeros of f(x)=x2-5x+k, such that alfa-beta=1, find k

Answer 1

alpha + beta =5
alpha - beta = 1
solving this...
2*alpha = 6
alpha = 3
so beta= 2
hence k= 3*2=6

Answer 2

F(x) = x2 - 5x + k
α- β = 1........i

Then using relation between zeros and co efficients,

α +β = 5..........ii
αβ = k.......iii

Solving i and ii

α + β = 5
α - β = 1
. .................
2α= 6
α= 3

Then β = 2

Substituting the values of α and β in iii

3*2 = K
Therefore k = 6


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