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:

To find an unknown coefficient in a polynomial, substitute the given root into the equation and solve for the variable.

Answer 1

The Correct Option is B

Substituting \( x = 1 \) into the polynomial:
\[ a(1)^2 - 3(a-1)(1) - 1 = 0. \] \[ a - 3a + 3 - 1 = 0. \] \[ -2a + 2 = 0. \] \[ a = 1. \]