One root of the following given equation $2{x^5} - 14{x^4} + 31{x^3} - 64{x^2} + 19x + 130 = 0$ is
$1$
$3$
$5$
$7$
If $|x - 2| + |x - 3| = 7$, then $x =$
The solutions of the quadratic equation ${(3|x| - 3)^2} = |x| + 7$ which belongs to the domain of definition of the function $y = \sqrt {x(x - 3)} $ are given by
Let $a, b, c, d$ be numbers in the set $\{1,2,3,4,5,6\}$ such that the curves $y=2 x^3+a x+b$ and $y=2 x^3+c x+d$ have no point in common. The maximum possible value of $(a-c)^2+b-d$ is
If $a,b,c$ are distinct real numbers and $a^3 + b^3 + c^3 = 3abc$ , then the equation $ax^2 + bx + c = 0$ has two roots, out of which one root is
The sum of all non-integer roots of the equation $x^5-6 x^4+11 x^3-5 x^2-3 x+2=0$ is