Possibility of integral quadratic with these roots

Question

If x and w are the roots of a quadratic equation with integral coefficients then is this possible: ${x = w = \frac{2}{3}}$. The correct answer says it is, but how is that so if it means: ${(x-\frac{2}{3})^2}$ which would simplify to non-integral coefficients.

Answer 1

In general any time you have a polynomial with all rational roots, you can rewrite the polynomial as a polynomial with all integer coefficients with the same roots by multiplying $p(x) = \prod_i (x - q_i)$ by the product of the denominators of the rational roots $q_i$.

Answer 2

$$(x-2/3)^2=0$$ $${x^2-2\cdot(2/3)x+(2/3)^2}=0$$ $$x^2-(4/3)x+(4/9)=0/\cdot9$$ $$9x^2-12x+4=0$$ is equation with integer coefficients