Finding a quadratic equation:
If roots are reciprocals of roots of equation $$ax^2 + bx + c = 0$$, then equation is $$cx^2 + bx + a = 0$$
If roots are k more than roots of $$ax^2 + bx + c = 0$$ then equation is $$a(y-k)^2 + b(y-k) + c = 0$$
If roots are k times roots of $$ax^2 + bx + c = 0$$ then equation is $$a(y/k)^2 + b(y/k) + c = 0$$
If roots are negatives of roots of ax²+bx+c=0, new equation is ax²−bx+c=0
If p and q are roots of ax²+bx+c=0, and we want a new equation whose roots are p² and q². The equation will be $$a^2x^2−(b^2−2ac)x+c^2=0$$
