State whether the following statements are true or false. Justify your answers.
$(i)$ Every quadratic equation has exactly one root.
$(ii)$ Every quadratic equation has at least one real root.

(N/A) $(i)$ False. $A$ quadratic equation of the form $ax^{2} + bx + c = 0$ (where $a \neq 0$) has exactly two roots,which may be real or complex.
$(ii)$ False. $A$ quadratic equation does not necessarily have a real root. For example,the equation $x^{2} + 4 = 0$ has no real roots because $x^{2} = -4$,and the square of a real number cannot be negative.