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Question

Find rational roots of the polynomial f(x) = 2x3 + x2 − 7x − 6.

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Solution

The given polynomial is


f(x) is a cubic polynomial with integer coefficients. If bc is rational root in lowest terms, then the values of b are limited
to the factors of 6 which are ±1,±2,±3,±6 and the values of c are limited to the factor of 2 as ±1,±2. Hence, the possible
rational roots are ±1,±2,±3,±6,±12,±32 .

Since,

So, 2 is a root of the polynomial

Now, the polynomial can be written as,

Also,

Therefore,

Hence, the rational roots of the polynomialare 2, – 3/2 and – 1.


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