Question

Find a polynomial function that has the given zeros:
(1 + sq. root 3, 1 - sq. root 3)

Answer 1

2 zeroes means , it is a polynomial of degree 2 , i.e. , it is quadratic polynomial.

Answer 2

the general form of a quadratic polynomial-
\[x^{2}-(\alpha +\beta)x+\alpha \beta=0\] where \[\alpha\]and\[\beta\]are the zeroes/roots of the polynomial.

Here,
\[\alpha = 1+\sqrt{3}\]\[\beta = 1-\sqrt{3}\]

so substitute the values of alpha an beta in the general form to get the desired polynomial.