Two numbers, a a a and b b b , are such that the quadratic equation a x 2 + 3 x + 2 b = 0 a x^2 + 3x + 2b = 0 a x 2 + 3 x + 2 b = 0 has roots whose su...

If the equations $$x^2 + mx + 9 = 0$$, $$x^2 + nx + 17 = 0$$, and $$x^2 + (m+n)x + 35 = 0$$ have a c...

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 equatio...

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

The quadratic function $$ f(x) = ax^2 + bx + c $$, where $$ a < 0 $$, has two distinct roots select...

If $$(a + b\sqrt{3})^2 = 52 + 30\sqrt{3}$$, where $$a$$ and $$b$$ are natural numbers, then $$a + b...