Find apolynomial function of degree3 f(10)=17,and thezeros are 0,5 and8

Given:

Degree of a polynomial = 3

Zeros of the polynomial = 0,5,8

f(10)=17

To find:

The polynomial function.

Solution:

The general form of a polynomial is

Where, a is a constant, are zeros with multiplicity respectively.

Since, 0,5,8 are zeros of the polynomial, therefore, (x-0),(x-5), (x-8) are the factors of required polynomial.

          ...(i)

Putting x=10, we get

We have f(10)=17.

Putting a=0.17 in (i).

Therefore, the required polynomial is .

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