Quadratic Equat...

The equation $$(a+2){x}^{2}+(a-3)x=2a-1,a\neq -2$$ has rational roots for 

If $$\displaystyle ax^{2}+bx+6=0$$ does not have two distinct real roots, where $$a\in R,b\in R$$, then the least value of $$3a+b$$ is

If the roots of the equation $$x^{2} + a^{2} = 8x + 6a$$ are real, then:

Which of the following is not a quadratic equation?

If both 'a' and 'b' belong to the set $$\left \{ 1, 2, 3, 4 \right \}$$, then the number of equations of the form $$ax^{2}+bx+1=0$$ having real roots is:

If the equation $$4x^{2} + x(p + 1) + 1 = 0$$ has exactly two equal roots, then one of the values of $$p$$ is

The value of $$x^{2} - 6x + 13$$ can never be less than

If $$\displaystyle ax^{2}+bx+1= 0, a \in R, b\in R,$$ does not have distinct real roots, then the maximum value of $$b^2$$ is

The number of values of $$k$$ for which $$\displaystyle \left \{x^{2}-(k-2)x+k^{2}\right\}+ \left \{x^{2}+kx+(2k-1)\right \}$$ is a perfect square is/are 

If at least one of the equations $$ { x^{ 2 } }+px+q=0$$ , $$ { x^{ 2 } }+rx+s=0 $$ has real roots, then