Find a polynomial of degree n that has only the given zero(s).
We will use the concept of factors of the polynomial to find the polynomial.
Answer: The standard polynomial will be (x - a1) (x - a2) (x - a3).......(x - an) with a1, a2 ,...an as their zeroes.
Let's see how we will use the concept of factors of the polynomial to find the polynomial.
When any polynomial is factorized, then the polynomial is segmented into its factors. When the factors are multiplied among themselves, then we get parent polynomial.
Then the polynomial will be equal to (x - a1) (x - a2) (x - a3).......(x - an) --(1)
We can understand better by taking a random example.
Let us consider a polynomial of degree 3 with -4, 3, and -5 as their zeroes.
so we can write x = - 4 , x = 3, x = -5
Therefore, the required polynomial will be (x + 4) (x - 3) (x + 5) [ From equation (1) ]