The complete solution of the inequation ${x^2} - 4x < 12\,{\rm{ is}}$
$x < - \,2$ or $x > 6$
$ - \,6 < x < 2$
$2 < x < 6$
$ - \,2 < x < 6$
If $a, b, c, d$ and $p$ are distinct real numbers such that $(a^2 + b^2 + c^2)\,p^2 -2p\, (ab + bc + cd) + (b^2 + c^2 + d^2) \le 0$, then
Suppose the quadratic polynomial $p(x)=a x^2+b x+c$ has positive coefficient $a, b, c$ such that $b-a=c-b$. If $p(x)=0$ has integer roots $\alpha$ and $\beta$ then what could be the possible value of $\alpha+\beta+\alpha \beta$ if $0 \leq \alpha+\beta+\alpha \beta \leq 8$
Let $a, b, c$ be non-zero real roots of the equation $x^3+a x^2+b x+c=0$. Then,
The smallest value of ${x^2} - 3x + 3$ in the interval $( - 3,\,3/2)$ is
If $x$ be real, then the minimum value of ${x^2} - 8x + 17$ is