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If x = 1 is a zero of the polynomial then f(1) = 0.
p(1)^2 - 3(p - 1) * 1 - 1 = 0
p - 3p + 3 - 1 = 0
-2p + 2 = 0
-2p = -2
p = 1
Therefore the value of p = 1.
Hope this helps!