Question

Find a polynomial of degree n that has only the given zero(s). (There are many correct answers.) x = −1, 8, 9, 5; n = 5

Answer 1

Given :

Solutions of polynomial x = -1, 8, 9, 5 .

To Find :

A polynomial with given roots.

Solution :

We know, polynomial of zeroes x1, x2 , x3 ....... xn is given by :

$y=(x-x1)(x-x2)(x-x_3).........(x-xn)$

So, for given zeroes equation is :

$y=(x-(-1))(x-8)(x-9)(x-5)\\\\y=(x+1)(x-8)(x-9)(x-5)$

Therefore, degree of polynomial is 4 ( equal to number of zeroes ).

Hence, this is the required solution.