Question 1072645

Given that the equation x(x-2p)=q(x-p) has real roots for all real values of p and q. If q=3, find a non-zero value for p so that the roots are rational.
<pre>For the roots to be rational, the discriminant must be = 0, or a positive PERFECT SQUARE integer, such as 1, or 4, or 9, etc.
When the discriminant is set as &#8805; 0, the result is the following quadratic inequality: {{{4p^2 + 9 >= 0}}}
Solving for p gives 2 IMAGINARY numbers.