Question

Quadratic polynomials with rational coefficients having `sqrt(3)` as a zero are given by ______.

Answer 1

Quadratic polynomials with rational coefficients having `sqrt(3)` as a zero are given by k(x² – 3), where k is a constant.

Explanation:

If `sqrt(3)` is a root and coefficients are rational, its conjugate `-sqrt(3)` must also be a root, so the quadratic is `(x - sqrt(3))(x + sqrt(3)) = x^2 - 3`, up to multiplication by a rational constant.