SOLUTION: If 1 is a zero of p(x) =ax^3-(a-1)x-1 then find value of a

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Question 1003361: If 1 is a zero of p(x) =ax^3-(a-1)x-1 then find value of a
Found 3 solutions by mananth, ikleyn, MathTherapy:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website!

p(x) =ax^3-(a-1)x-1
since 1 is the root
p(1) = a(1)^3-(1-1)x -1
=a-1
by remainder theorem
a-1 = 0
therefore a=1

Answer by ikleyn(53742)   (Show Source):
You can put this solution on YOUR website!
.
If 1 is a zero of p(x) = ax^3-(a-1)x-1 then find value of a
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In his post, @mananth deduces that, under given condition, the value of ' a ' must be 1.

        It is a crude and a danger logical mistake.

Actually, a ' 1 ' is a root of a polynomial   p(x) = ax^3 - (a-1)x - 1 for value of ' a ',

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

So, from the given condition, we can not determine a value of ' a ' : it can be number/value.

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

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

Answer by MathTherapy(10801)   (Show Source):
You can put this solution on YOUR website!

If 1 is a zero of p(x) =ax^3-(a-1)x-1 then find value of a ********************************************************** Given that 1 is a 0/1 is a solution, becomes: --- Substituting 1 for x 0 = a - a + 1 - 1 ------ Substituting 0 for p(1), and simplifying 0 = 0 (TRUE) As the above equation proves TRUE, there's NO 1 SPECIFIC value for "a." As such, ANY value of "a" will SATISFY the function,