Question:
If 1 is a zero of the polynomial $a x^{2}-3(a-1) x-1$, then find the value of $a$.
Solution:
Given: x = 1 is one zero of the polynomial ax2 − 3(a − 1) x − 1
Therefore, It will satisfy the above polynomial.
Now, we have
$a(1)^{2}-3(a-1) 1-1=0$
$\Rightarrow a-3 a+3-1=0$
$\Rightarrow-2 a=-2$
$\Rightarrow a=1$