Location of Roots

The values of $k$ for which each root of the equation $x^2-6kx+2-2k+9k^2=0$ is greater than $3$ , always satisfy the inequality

Given $f\left(x\right)=x^2+\left(a+2\right)x+a^2-a+2$ and $f\left(-2\right)<0$.  Then $a$ lies in the interval:

The values of $\text{'}\mathrm{a}\text{'}$ for which the roots of the equation ${\mathrm{x}}^2+\mathrm{x}+\mathrm{a}=0$ are real and exceed $\text{'}\mathrm{a}\text{'}$ are -

For the given equation $2x^3+3x+k=0$, what are the values of $k$ so that it contains two distinct real roots in the interval $\left[0,1\right]:$

The range of $a$ for which the equation $x^2+ax-4=0$ has its smaller root in the interval $\left(-1,\mathrm{ }2\right)$ is

If $2$ lies between both the roots of $x^2-\left(\lambda +1\right)x+{\lambda }^2+\lambda -8=0$, then 

Consider the function $f\left(x\right)=\frac{x^3}{4}-\sin \pi x+3$

Consider the inequality $x^2-2x+a-5<0$, for at least one negative value of $x$, the complete set of values of ‘$a$’ is:

If both roots of the quadratic equation $x^2=mx-4$ are real and distinct and they lie in the interval $\left(1,5\right),$ then $m\in$_____

Note: In the actual JEE paper interval was $\left[1, 5\right]$

If the roots of the quadratic equation $x^2-2ax+a^2=3-a$ are real and less than $3$, then

Let $S$ denotes the set of all real values of $a$ for which the roots of the equation $x^2-2ax=1-a^2$ lie between $5$ and $10$, then $S$ equals to :

Let $a, b, c$ be real numbers, $a\ne 0$ if $\alpha$ is a root of the equation $a^2{x}^2+bx+c=0$, $\beta$ is a root of  the equation $a^2{x}^2-bx-c=0$ and $0<\alpha <\beta ,$ then the equation $a^2{x}^2+2bx+2c=0$ has a root $\gamma$ which satisfies the relation.

For the given equation $2x^3+3x+k=0$, what are the values of $k$ so that it contains two distinct real roots in the interval $\left[0,1\right]:$

Let $f\left(x\right)=\left(a^2+a+2\right)x^2-(a+4)x-7, x\in R.$ If unity lies between the roots of equation $f\left(x\right)=0$ then find total integral values of $a$.

If ${\mathrm{x}}_1, {\mathrm{x}}_2$ are roots of ${\mathrm{x}}^2-3\mathrm{x}+\mathrm{a}=0, \mathrm{a}\in \mathrm{R}$ and ${\mathrm{x}}_1<1<{\mathrm{x}}_2$, then the value of $a$ lies in the interval

 What is the range of values of $\mathrm{a}$, for which $e^{\left|\sin x\right|}+e^{-\left|\sin x\right|}+4\mathrm{a}=0$ has exactly $4$ different solutions in the interval $[0,2\mathrm{\pi }]$?

The set of values of $a$ for which $2$ lies between the roots of the quadratic equation $x^2+\left(a+2\right)x-\left(a+3\right)=0$, is 

If $p, q$ and $r$ are positive rational numbers such that $p>q>r$ and the quadratic $(p+q-2r)x^2+(q+r-2p)x+(r+p-2q)=0$ has a root in $(-1, 0)$, then which of the following statements hold good?

Given $f\left(x\right)=x^2+\left(a+2\right)x+\left(a^2-a+2\right)$. If both roots of the equation $f\left(x\right)=0$ lie in interval $\left(0,\infty \right)$, then range of $a$ is: