1.48: Relationships between roots

Given that $\alpha+\beta=5$ and $\alpha^2+\beta^2=19$

(a) show that $\alpha\beta=3$. (2)

(b) Hence form a quadratic equation, with integer coefficients, which has roots $\alpha$ and $\beta$. (2)

(c) Form a quadratic equation, with integer coefficients, which has roots $\dfrac\alpha\beta$ and $\dfrac\beta\alpha$. (5)