Quadratic Equat...

If $$1$$ is a root of the equations $$ay^2$$ + $$ay + 3 = 0$$ and $$y^2$$+ $$y + b = 0$$, then find the value of $$ab$$

The ratio of the roots of the equation $$ { ax }^{ 2 }+bx+c=0$$ is same as the ratio of the roots of equation $$ { px }^{ 2 }+qx+r=0$$. If $$ { D }_{ 1 }$$ and $$ { D }_{ 2 }$$ are the discriminants of   $$ { ax }^{ 2 }+bx+c=0$$  and $$ { px }^{ 2 }+qx+r=0$$ respectively, then $$ { D }_{ 1 }:{ D }_{ 2 }=$$

Let $$a, b, c$$ be the lengths of sides of a scalene triangle. If the roots of the equation $$\displaystyle x^{2}+2(a+b+c)x+3\lambda (ab+bc+ca)=0$$ $$(\lambda \in R)$$ are real then

The equation $$\sqrt {2x-2x^2-5}=x^2-2x-3$$, where $$x$$ is real has 

If $${ x }^{ 2 }-\left( a+b+c \right) x+\left( ab+bc+ca \right) =0$$ has non real roots, where $$a,b,c\in { R }^{ + }$$, then $$\sqrt { a } ,\sqrt { b } ,\sqrt { c } $$

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

On solving $$4x^2 - 4a^2x + (a^4 - b^4)$$ = 0 we get value of $$x$$ is equal to

If $$\alpha, \beta$$ are the roots of $$\displaystyle ax^{2}+2bx+c=0$$ and that of $$\displaystyle Ax^{2}+2Bx+C=0$$ be $$\displaystyle \alpha+\delta, \beta +\delta $$ then the value of $$\displaystyle \frac{b^{2}-ac}{B^{2}-AC} $$ is

The roots of the equation $$\displaystyle \left ( x-a \right )\left ( x-b \right )+\left ( x-b \right )\left ( x-c \right )+\left ( x-c \right )\left ( x-a \right )=0$$ are

If the quadratic equation $$\displaystyle x^{2}-mx-4x+1=0$$ has real and distinct roots, then the values of $$m$$ are
A.  $$\displaystyle (-\infty , -6)$$
B.  $$\displaystyle (-\infty,-3)$$