Question 1003361
.
If 1 is a zero of p(x) = ax^3-(a-1)x-1 then find value of a
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~



In his post, @mananth deduces that,  under given condition,  the value of  ' a '  must be  1.

<H3>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is a crude and a danger logical mistake.</H3>

Actually, &nbsp;a &nbsp;' 1 ' &nbsp;is a root of a polynomial  &nbsp;&nbsp;p(x) = ax^3 - (a-1)x - 1  &nbsp;for  &nbsp;{{{highlight(highlight(ANY))}}}  &nbsp;value of &nbsp;' a ',


Indeed,  &nbsp;for every such a polynomial &nbsp;p(x),  &nbsp;&nbsp;p(1) = a - (a-1) - 1 === 0  &nbsp;identically for any value of &nbsp;'a'.


So, from the given condition, &nbsp;we can not determine a value of &nbsp;' a ' :  it can be &nbsp;{{{highlight(highlight(ANY))}}}  &nbsp;number/value.



I don't know if this problem is a mathematical joke or a &nbsp;TRAP &nbsp;to catch 
a hapless student, &nbsp;or a mistake of the problem's creator, &nbsp;but what I said is the &nbsp;FACT.



If it is a &nbsp;trap, &nbsp;then @mananth has fallen in this trap and invites all his readers to follow him.