If $x$ is real,then the minimum value of ${x^2} - 8x + 17$ is

Let $a, b$ and $c$ be the sides of a scalene triangle. If $\lambda$ is a real number such that the roots of the equation $x^2+2(a+b+c)x+3\lambda(ab+bc+ca)=0$ are real,then the interval in which $\lambda$ lies is

The solution set of the congruence $8x \equiv 6 \pmod{14}$,where $x \in \mathbb{Z}$,is:

If the sum of two roots $\alpha, \beta$ of the equation $x^4-x^3-8 x^2+2 x+12=0$ is zero and $\gamma, \delta$ $(\gamma > \delta)$ are its other roots,then $3 \gamma+2 \delta=$

The roots of the equation $x^{2/3} + x^{1/3} - 2 = 0$ are

If $a, b$ are real numbers and $\alpha$ is a real root of $x^2 + 6x + 12 + 3 \sin(a + b\alpha) = 0$,then the value of $\cos(a + b\alpha)$ for the least positive value of $a + b\alpha$ is