Let $$\alpha$$, $$\beta$$ be the roots of the equation x² $$-$$ 6x $$-$$ 2 = 0 with $$\alpha$$ > $$\beta$$. If a_n = $$\alpha$$ⁿ $$-$$ $$\beta$$ⁿ for n $$\ge$$ 1, then the value of $${{{a_{10}} - 2{a_8}} \over {2{a_9}}}$$ is

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