The expression ax² + bx + c (a, b and c are real) has the same sign as that of a for all x if

Let z₁ and z₂ be two imaginary roots of z² + pz + q = 0, where p and q are real. The points z₁, z₂ and origin form an equilateral triangle if

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,