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Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

Since α and β are zeros of the polynomial the polynomial is (x-α)(x-β). therefore p(x) = (x-α)(x-β) x^2-5x+k = (x-α)(x-β) x^2-5x+k = x^2-(α+β)x+αβ equating the coefficients of x on both sides we get, α+β = 5....(1) equating the constants on both sides we get αβ = k ...(2) We have α-β = 1 .....(3) Solving (1) and (3) we get α=3 and β = 2 therefore k = αβ =3*2 = 6