How do you use the rational root theorem to find the roots of #x^3 + 2x^2 + 3x + 6 = 0 #?

1 Answer
Jul 5, 2016

-2, #+-isqrt3#


The degree of the polynomial on then left side is odd and the coefficient of its leading term is 1, hence the product of the roots would be -6, these can be #+-1, +-2, +-3, +-6#.

Out of these values x= -2 makes the polynomial on the left side 0, hence x+2 would be factor of the polynomial. Now divide the polynomial by x+2,
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From this factorisation, the roots can be writtne as -2, #+-isqrt3#