Write whether the following statements are true or false. Justify your answers.
$(i)$ If the coefficient of $x^{2}$ and the constant term have the same sign and if the coefficient of $x$ term is zero,then the quadratic equation has no real roots.
$(ii)$ Every quadratic equation has at least two roots.

(A) $(i)$ True. For a quadratic equation $ax^{2} + bx + c = 0$,the discriminant is $D = b^{2} - 4ac$. Given $b = 0$,we have $D = -4ac$. If $a$ and $c$ have the same sign,then $ac > 0$,which implies $D = -4ac < 0$. Since the discriminant is negative,the equation has no real roots.
$(ii)$ False. $A$ quadratic equation has exactly two roots (which may be real and distinct,real and equal,or complex/imaginary). It does not necessarily have "at least" two roots in the context of real numbers,and it cannot have more than two roots.