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
Consider the cubic equation $x^3+c x^2+b x+c=0$ where $a, b, c$ are real numbers. Which of the following statements is correct?
The equation $e^{4 x}+8 e^{3 x}+13 e^{2 x}-8 e^x+1=0, x \in R$ has:
If ${x^2} + 2ax + 10 - 3a > 0$ for all $x \in R$, then
Let $\alpha$ and $\beta$ be the roots of the equation $5 x^{2}+6 x-2=0 .$ If $S_{n}=\alpha^{n}+\beta^{n}, n=1,2,3 \ldots$ then :
Product of real roots of the equation ${t^2}{x^2} + |x| + \,9 = 0$