Answer:
Step-by-step explanation:
Given is an algebraic polynomial of degree 5.
Here leading term is p=3 and constant term is q =12
Factors of p are ±1,±2,±3
Factors of q are
Possible forms of p/q will be the same for any other polynomial of degree 5 with leading term =3 and constant term = 12
Hence any other polynomial
will have same possible zeroes of p/q, when a,b,c are rational.
Hence any polynomial of this type would have the same possible rational roots.
Solution:
we have been asked to verify that -5, 1/2, and 3/4 are the zeroes of the cubic polynomial
To verify that whether the given values are zeros or not we will substitute the values in the given Polynomial, if it will returns zero, it mean that value is Zero of the polynomial. But if it return any thing other than zeros it mean that value is not the zero of the polynomial.
Let
Hence -5, 1/2, and 3/4 are not the zeroes of the given Polynomial.
Since sum of roots
But
Hence we do not find any relation between the coefficients and zeros.
Anyway if the given values doesn't represents the zeros then those given values will not have any relation with the coefficients of the p[polynomial.