If 1 is a zero of the polynomial p(x) = ax^{2} – 3(a – 1) x – 1, then find the value of a.

Given,

p(x) = ax^{2} – 3(a – 1) x – 1

Zero is 1

Now,

p(1) = a(1)^{2} – 3(a – 1) ×1 – 1 = 0

p(1) = a – 3a + 3 – 1 = 0

p(1) = – 2a + 2 = 0

= – 2a = – 2

= a = – 2/ – 2 = 1

So the value of a = 1

30