# Find rational roo

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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