Question 124
Determine the value of the real parameter $p$ so that the solutions of
$$
(p - 3)x^2 + (p^2 + 1)x - 11p + 18 = 0
$$
are the lengths of legs of a right-angled triangle with hypotenuse of length $\sqrt{17}$.
$$
(p - 3)x^2 + (p^2 + 1)x - 11p + 18 = 0
$$
are the lengths of legs of a right-angled triangle with hypotenuse of length $\sqrt{17}$.