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Question

It is given that the polynomial p(x)=x3−9x2+26x+24 has zeroes that are integers. Which of the following is not a zero of the polynomial.

A
5
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B
3
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C
4
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D
2
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Solution

The correct option is A 5
Let the zeros of the polynomial be a, b and c. Then,
p(x)=(xa)(xb)(xc)

The constant term of the polynomial is abc=24.
Also, it is given that a, b and c, all are integers.
So, the zeroes of the polynomial are factors of 24. Possible zeroes are:
±1,±2,±3,±4,±6,±12,±24

Clearly, 5 is not a zero of the polynomial.

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