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Rational Zero Theorem

1. P(x)= 5x3- x2- 15x +3
2. P(x)= 2x4+ 9x3 + 15x2 + 11x +3
3. P(x)= 3x5- x4 + 6x3 -2x2 +8x -5
4. P(x)= 6x4 +11x3 + 8x2 -6x -4

Thanks!

Sagot :

SugoiOverloadidn
I'll solve the first one and leave the rest for you to practice on.

The Ratonal Zero Theorem states that the set of possible rational roots can be derived from dividing the factors of the constant coefficiant by the fators of the leading coefficient.  Let p be the set containing factors of the constatnt coefficient and q be the set containing the factors of the leading coefficient.

p = {-3, -1, 1, 3}
q = {-5, -1, 1, 5}

Thus, p/q = {3/5, -3/5, 1/5, -1/5, 3, -3, 1, -1}