Quadratic Equat...

Which constant must be added and subtracted to solve the quadratic equation $$\displaystyle 9x^2 +\frac{3}{4}x+ 2 = 0$$ by the method of completing the square?

Assertion (A): The equation $$x-\displaystyle \cfrac{2}{x-1}=1-\cfrac{2}{x-1}$$ has no root.
Reason (R): $$x-1\neq 0$$, then only above equation is defined.

lf the roots of $${p}{x}^{2}+2{q}{x}+{r}=0$$ and $$qx^{2}-2\sqrt{pr}x+q=0$$ are simultaneously real, then

If $$a > 0$$, then the expression $$ax^{2}+bx+c$$ is positive for all values of $$x$$ provided

If the expression $$(a-2)x^{2}+2(2a-3)x+(5a-6)$$ is positive for all real values of $$x$$, then

Which of the following is not a quadratic equation :

If $$a=0$$, then the equation $$\displaystyle \frac{x-a-1}{x-a}=a +1-\displaystyle \frac{1}{x-a}$$ has

Which of the following is not a quadratic equation? 

Values of $$k$$ for which the quadratic equation $$2x^2+ kx + k = 0$$ has equal roots.

If $$14$$ is the maximum of $$-\lambda x^{2} +  \lambda x + 8$$, then the value of $$\lambda$$ is