Quadratic Equat...

Find the roots of the following equations, if they exist, by the completing the square:

Find the root of the following quadratic equation, if they exist, by the method of completing the square.
$$2x^2+x-4=0$$.

The root of $$x^{2}+kx+k=0$$ are real and equal , find $$k$$.

Identify the standard form of the given equation$$(4x-5)(4x+5)=0$$.

If both roots of quadratic equation $$(\alpha +1)x^{2}-2(1+3\alpha )x+1+8\alpha =0$$ are real and distinict, the $$\alpha$$ be- 

If $$a,b,c,x$$ are real numbers and $$\left( { a }^{ 2 }+{ b }^{ 2 } \right) { x }^{ 2 }-2b\left( a+c \right) x+\left( { b }^{ 2 }+{ c }^{ 2 } \right) =0$$ has real & equal roots, then $$a,b,c$$ are in 

Roots of the equation $$\sqrt {\dfrac {x}{1-x}}+\sqrt {\dfrac {1-x}{x}}=2\dfrac {1}{6}$$ are

Let $${ \lambda  }_{ 1 }$$ and $${\lambda}_{2}$$ be two values of $${\lambda}$$ for which the expression $${x}^{2}+(2-\lambda)x+\lambda-{3}$$ becomes a perfect square. The value of $$(\lambda_{1}^{2}+\lambda_{2}^{2})$$ equals

The discriminant of the quadratic equation $$5 x ^ { 2 } - 6 x + 1 = 0$$ is

$$\begin{array} { l } { \text { If } \alpha , \beta \text { are the roots of } a x ^ { 2 } + b x + c  \text { and } \alpha + h } , { \beta + h \text { are the roots of } p x ^ { 2 } + q x + r = 0 }  \\{ \text { and } D _ { 1 } \text { , } D _ { 2 } \text { are the respective } }  { \text { discriminants of these equations, } } \\  { \text { then } D _ { 1 } : D _ { 2 } = } \end{array}$$