KöMaL 2022 B5280

Let $a>2$, $b$ and $c$ be real numbers. Consider the three statements below. (1) The equation $ax^2 + bx + c = 0$ has no real solution. (2) The equation $(a-1)x^2 + (b-1)x + (c-1) = 0$ has 1 real solution. (3) The equation $(a-2) x^2 + (b-2)x + (c-2) = 0$ has 2 real solutions. $a)$ Given that statements (1) and (2) are true, can we conclude that statement (3) is also true? $b)$ Given that statements (2) and (3) are true, can we conclude that statement (1) is also true?