Question

The quadratic equation with rational coefficients having `sqrt(3)/2` as a root is ______.

Answer 1

The quadratic equation with rational coefficients having `sqrt(3)/2` as a root is 4x² – 3 = 0.

Explanation:

Let `x = sqrt(3)/2`.

Then `x^2 = 3/4`.

So `x^2 - 3/4 = 0`. 

Multiplying by 4 gives 4x² – 3 = 0, which has rational coefficients its roots are `±sqrt(3)/2`.