Quadratic Equations

Two numbers, $$a$$ and $$b$$, are such that the quadratic equation $$a x^2 + 3x + 2b = 0$$ has roots whose sum is $$-6$...

If $$x$$ is a real number, find the smallest value of the expression $$3x^2 - 4x + 7$$. ...

The expression $$ a^2 + ab + b^2 $$ is ________ for $$ a < 0 $$ , $$ b < 0 $$. ...

A quadratic equation $$x^2 + bx + 12 = 0$$ has 2 as one of its roots, and another quadratic equation $$x^2 + bx + q = 0...

The quadratic function $$ f(x) = ax^2 + bx + c $$, where $$ a < 0 $$, has two distinct roots selected from the set $$\{...