Quadratic Equat...

Given that $$r$$ and $$s$$ are constants , the solution of the quadratic equation, $$r{x}^{2}=\dfrac{1}{s}x+3$$ , is:

The equation $$\displaystyle 9y^{2}(m+3)+6(m-3)y+(m+3)=0 $$, where $$m$$ is real has real roots then 

A ray emanating from (6,2) is incident on ellipse $$\displaystyle \frac{(x-1)^{2}}{45}+\frac{(y-2)^{2}}{20}=1$$ at (4.6) The equation of reflected ray (after 1st reflection ) is  

The sum of all roots of the roots of the equations $$\displaystyle |x-1|^{2}-5|x-1|+6=0$$ is 

Solve the  equation: $$3+\dfrac {30}{{x}^{2}}=-\dfrac {21}{x}$$

If $$(1+2x+x^2)^n=\displaystyle\sum^{2n}_{r=0}a_rx^r$$, then $$a_r=$$.

If the expression $$x^2+2(a+b+c)x+3(bc+ca+ab)$$ is a perfect square, then

Number of possible value(s) of integer '$$a$$' for which the quadratic equation $$x^2+ax+16=0$$ has equal roots, is

Equation $$x^2 - x + q = 0$$ has imaginary roots if 

Discriminant is_________ for the quadratic equation $$x+\dfrac { 1 }{ x } =-5$$.