If for a posiive integer $n$ , the quadratic equation, $x\left( {x + 1} \right) + \left( {x + 1} \right)\left( {x + 2} \right) + .\;.\;.\; + \left( {x + \overline {n - 1} } \right)\left( {x + n} \right) = 10n$ has two consecutive integral solutions, then $n$ is equal to:
$11$
$12$
$9$
$10$
What is the sum of all natural numbers $n$ such that the product of the digits of $n$ (in base $10$ ) is equal to $n^2-10 n-36 ?$
Below are four equations in $x$. Assume that $0 < r < 4$. Which of the following equations has the largest solution for $x$ ?
The number of distinct real roots of the equation $x^{5}\left(x^{3}-x^{2}-x+1\right)+x\left(3 x^{3}-4 x^{2}-2 x+4\right)-1=0$ is
The number of real roots of the equation $x | x |-5| x +2|+6=0$, is
If $a < 0$ then the inequality $a{x^2} - 2x + 4 > 0$ has the solution represented by