Find rational roots of the polynomial f(x) = 2x3+x2-7x-6.
We have,
f(x) = 2x3+x2-7x-6
Clearly, f (x) is a cubic polynomial with integer coefficients. If 
is a rational root in lowest term, then the value of b are limited to the factors of 6 which are 
and values of c are limited to the factors of 2 which are 
.
Hence, the possible rational roots of f(x) are:
We observe that,
f (-1) = 2 (-1)3 + (-1)2 – 7 (-1) – 6
= -2 + 1 + 7 – 6
= 0
f (2) = 2 (2)3 + (2)2 – 7 (2) – 6
= 16 + 4 – 14 – 6
= 0
f (
) = 2 (
)3 + (
)2 – 7 (
) – 6
= 
+ 
+ 
– 6
= 0
Hence, -1, 2, 
are the rational roots of f (x).
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