If $x$ is real, then the value of ${x^2} - 6x + 13$ will not be less than

The number of distinct real roots of $x^4-4 x^3+12 x^2+x-1=0$ is

Complete solution set of the inequality $\left( {{{\sec }^{ - 1}}\,x - 4} \right)\left( {{{\sec }^{ 1}}\,x - 1} \right)\left( {{{\sec }^{ - 1}}\,x - 2} \right) \ge 0$ is

Consider the equation $(1+a+b)^2=3\left(1+a^2+b^{2})\right.$ where $a, b$ are real numbers. Then,

Let $a, b, c$ be non-zero real roots of the equation $x^3+a x^2+b x+c=0$. Then,

Equation $\frac{3}{{x - {a^3}}} + \frac{5}{{x - {a^5}}} + \frac{7}{{x - {a^7}}} = 0,a > 1$ has