How do you find the rational zeros of a polynomial

Rational zero test or rational root test provide us with a list of all possible real zer.We'll start with the small integers first.A rational zero is a zero that is also a rational number, that is, it is expressible in the form p q for some integers p,q with q ≠ 0.To find the zeros of a polynomial function, if it can be factored, factor the function and set each factor equal to zero.The rational zero theorem is a very useful theorem for finding rational roots.

If the remainder is not zero, discard the candidate.In fact the only rational roots it has are − 1 2 and 5 3.Problem zeros roots polynomial function rational zeros synthetic division background tutorials rational numbers and the number lineUse the rational zero theorem to list all possible rational zeros of the function.Polynomial functions with integer coefficients may have rational roots.

Suppose a is root of the polynomial p\left( x \right) that means p\left( a \right) = 0.in other words, if we substitute a into the polynomial p\left( x \right) and get zero, 0, it means that the input value is a root of the function.We can use the rational zeros theorem to find all the rational zeros of a polynomial.Note that in order for this theorem to work then the zero must be reduced to lowest terms.List all factors of the constant term and leading coefficient.8 36 46 7 − 12 − 4 − 1 8 28 18 − 11 − 1 − 3 = g ( − 1) ≠ 0 1 8 44 90 97 85 81 = g ( 1) ≠ 0 8 36 46 7 − 12 − 4 − 1 8 28 18 − 11 − 1 − 3 = g.

We now need to start the synthetic division work.To apply rational zero theorem, first organize a polynomial in descending order of its exponents.