If 1 is a zero of the polynomial

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

$a(1)^{2}-3(a-1) 1-1=0$

$\Rightarrow a-3 a+3-1=0$

$\Rightarrow-2 a=-2$

$\Rightarrow a=1$

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