Rational Root Theorem
Algebra
Level
3
If is a polynomial such that its coefficient of the leading term and the constant term are relatively prime, then can the polynomial have integer roots?
No
Yes
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For those,who don’t get it right,just think.
The Rational Root Theorem just says about the nature of numerator and denominator of a given rational root of a polynomial.
In my question,though c and a are relatively prime,does not imply that literally ’they’ are the only ’fractional’ roots.
Actually the immediate thing that the brain thinks is that as c and a are relatively prime,therefore there is no chance of the roots being integers.
Just think of the quadratic equation: x 2 + b x + c = 0 For many values of b and c, integer roots exist although c and a(here,1) are co-prime;for e.g. the equation x 2 − 5 x + 6 = 0 .