Question

If 1 is a zero of the polynomial p(x) = ax² − 3(a − 1) x − 1, then find the value of a. 

Answer 1

Given, 

p(x) = ax² − 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