The smallest value of ${x^2} - 3x + 3$ in the interval $( - 3,\,3/2)$ is
$3/4$
$5$
$-15$
$-20$
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
The roots of $|x - 2{|^2} + |x - 2| - 6 = 0$are
Let $t$ be real number such that $t^2=a t+b$ for some positive integers $a$ and $b$. Then, for any choice of positive integers $a$ and $b, t^3$ is never equal to
The polynomial equation $x^3-3 a x^2+\left(27 a^2+9\right) x+2016=0$ has
Suppose $m, n$ are positive integers such that $6^m+2^{m+n} \cdot 3^w+2^n=332$. The value of the expression $m^2+m n+n^2$ is