Question

If 1 is a zero of the polynomial $a x^{2}-3(a-1) x-1$ then find the value of $a.

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Answer

Given that 1 is a zero of the polynomial $ax^{2} - 3(a-1)x - 1$, we need to find the value of $a$.

Since 1 is a zero of the polynomial, we have: $$ p(1) = 0 $$

Substitute $x = 1$ into the polynomial: $$ a(1)^{2} - 3(a-1) \cdot 1 - 1 = 0 $$

Simplify inside the polynomial: $$ a - 3(a - 1) - 1 = 0 $$

Expand and combine like terms: $$ a - 3a + 3 - 1 = 0 $$

Combine the terms: $$ -2a + 2 = 0 $$

Solve for $a$: $$ -2a + 2 = 0 $$ $$ -2a = -2 $$ $$ a = \frac{-2}{-2} $$ $$ a = 1 $$

Therefore, the value of $a$ is 1.


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