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All possible roots of polynomial with in...

All possible roots of polynomial with integral coefficients can be identified by "RATIONAL ROOT TEST" according to rational root test if a plynomial ltbr. `a_(n)p^(n)+a_(n-1)p^(n-1)q+a_(n-2)p^(n-2)q^(2)+`…..`+a_(2)p^(2)q^(n-2)+a_(1)pq^(n-1)+a_(0)q^(n)=0`
Every term in above equation except possible the last one is divisible by `p` hence `p` should also divide `a_(0)q^(n)`, since `q` and `p` are relatively prime `p` must divide `a_(0)`. Similarly `q` also divides `a_(n)`. Now consider an equation `6x^(5)-19x^(4)-9x^(3)-16x^(2)+9x-1=0` and answer the following questions
Q. if given equation and equation `x^(3)+ax^(2)+ax+1=0` have two roots common then possible value(s) of is/are?

A

4

B

`(25)/(6)`

C

`(1)/(6)`

D

can not determine

Text Solution

Verified by Experts

The correct Answer is:
C
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