If $x$ is real, the expression $\frac{{x + 2}}{{2{x^2} + 3x + 6}}$ takes all value in the interval
$\left( {\frac{1}{{13}},\frac{1}{3}} \right)$
$\left[ { - \frac{1}{{13}},\frac{1}{3}} \right]$
$\left( { - \frac{1}{3},\frac{1}{{13}}} \right)$
None of these
Let $a$ be the largest real root and $b$ be the smallest real root of the polynomial equation $x^6-6 x^5+15 x^4-20 x^3+15 x^2-6 x+1=0$ Then $\frac{a^2+b^2}{a+b+1}$ is
Let $P(x) = x^3 - ax^2 + bx + c$ where $a, b, c \in R$ has integral roots such that $P(6) = 3$, then $' a '$ cannot be equal to
For what value of $\lambda$ the sum of the squares of the roots of ${x^2} + (2 + \lambda )\,x - \frac{1}{2}(1 + \lambda ) = 0$ is minimum
Let $r_1, r_2, r_3$ be roots of equation $x^3 -2x^2 + 4x + 5074 = 0$, then the value of $(r_1 + 2)(r_2 + 2)(r_3 + 2)$ is
The number of distinct real roots of the equation $|\mathrm{x}||\mathrm{x}+2|-5|\mathrm{x}+1|-1=0$ is....................