Mina O.

asked • 01/04/18

If k is a zero of the polynomial function

If k is a zero of the polynomial function
f(x)= ax4 – bx3 + cx2 – bx + a, then …… is also a zero of f

1) k + 1
2) k – 1
3) 1/ k
4) –k

1 Expert Answer

By:

Andy C. answered • 01/04/18

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Mina O.

Isn't 1/k  the solution since K doesn't equal 0?  so -k is not valid. 
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01/04/18

Andy C.

We do not know the value of k.
 
I prefer the term SOLUTION or ROOT instead of "zero".
The solution, root, or ZERO of the equation is the value of the
variable that makes the whole equation equal to zero.
 
For example, the equation X+2 has
root, solution zero of X=-2 since
-2 + 2 = 0
 
In this problem, we do not know what is the value of k.
All we know is that when X=k, the polynomial has value zero, 
as shown in the first step of my solution.
 
Next I divided everything by A, which cannot be zero,
otherwise, it would not even be there.
 
In the third step I rewrote subtraction as addition of the opposite.
 
In the fourth step that negative sign moves into the term containing
the K
 
Finally, the terms containing k can be rewritten as (-k) to
the same power.
 
This shows that when K is a root,solution, or zero to the 
polynomial, then so must -k
 
 
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01/04/18

Ghada A.

I think the solution will be 1/K because if you substitute with it, then multiply by K^4, you will get the same equation as with k. an additional point, when you substitute with -k, you change the sign of terms that contain b, so it cannot give you the same equation as k.
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05/31/19

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