If P(x) = ax² + bx + c and Q(x) = $$ - $$ax² + dx + c, where ac $$ \ne $$ 0 [a, b, c, d are all real], then P(x).Q(x) = 0 has

Let a, b, c be real numbers such that a + b + c < 0 and the quadratic equation ax² + bx + c = 0 has imaginary roots. Then,

If $${b_1}{b_2} = 2({c_1} + {c_2})$$ and b₁, b₂, c₁, c₂ are all real numbers, then at least one of the equations $${x^2} + {b_1}x + {c_1} = 0$$ and $${x^2} + {b_2}x + {c_2} = 0$$ has

The greatest integer which divides $$(p + 1)(p + 2)(p + 3)...(p + q)$$ for all $$p \in N$$ and fixed $$q \in N$$ is