MBAlad wrote:

Can someone explain how you arrived arrived at the solution for the quadratic? Keep it simple please brainiacs

Let me try...

The question can be rephrased as:

For how many real values of x can y be 0. In other words, we have to find out if the equation x^2+2qx+r = 0 has real roots, and if there are real roots, then how many are there?

A quadratic equation can have 0, 1 or 2 real roots....

Lets see how this is possible:

The formula for roots of a quadratic is given by:

x1 = [-b + sqrt(b^2-4ac)]/2a

x2 = [-b - sqrt(b^2-4ac)]/2a

As can be seen there are 0 real roots if b^2-4ac is -ve, because then each root includes an imaginary number.

There are 2 real roots if b^2-4ac is +ve

There is 1 real root if b^2-4ac = 0

With this knowledge, one should be able to solve the problem.