Question

If 1 is one zero of the polynomial \( p(x) = ax^2 - 3(a - 1)x - 1 \), then the value of \( a \) is:

• A. 3
• B. 1
• C. 0
• D. 2

Hint:

Substitute the given zero into the polynomial and solve for the unknown coefficient.

Answer 1

The Correct Option is B

Substitute \( x = 1 \) into the polynomial \( p(x) = ax^2 - 3(a - 1)x - 1 \): \[ a(1)^2 - 3(a - 1)(1) - 1 = 0. \] Simplify: \[ a - 3(a - 1) - 1 = 0 \quad \Rightarrow \quad a - 3a + 3 - 1 = 0 \quad \Rightarrow \quad -2a + 2 = 0 \quad \Rightarrow \quad a = 1. \] Thus, the value of \( a \) is \( \boxed{1} \).