If $$2a+3b+6c=0$$, then at least one root of the equation
$$a{x^2} + bx + c = 0$$ lies in the interval

A point on the parabola $${y^2} = 18x$$ at which the ordinate increases at twice the rate of the abscissa is

The real number $$x$$ when added to its inverse gives the minimum sum at $$x$$ equal :

If the function $$f\left( x \right) = 2{x^3} - 9a{x^2} + 12{a^2}x + 1,$$ where $$a>0,$$ attains its maximum and minimum at $$p$$ and $$q$$ respectively such that $${p^2} = q$$ , then $$a$$ equals