If the graph of $y = ax^3 + bx^2 + cx + d$ is symmetric about the line $x = k$ then

If two roots of the equation ${x^3} - 3x + 2 = 0$ are same, then the roots will be

Let $S$ be the set of all real roots of the equation, $3^{x}\left(3^{x}-1\right)+2=\left|3^{x}-1\right|+\left|3^{x}-2\right| .$ Then $\mathrm{S}$

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

Let $\mathrm{S}=\left\{x \in R:(\sqrt{3}+\sqrt{2})^x+(\sqrt{3}-\sqrt{2})^x=10\right\}$. Then the number of elements in $\mathrm{S}$ is :

If $x$ is real, the function $\frac{{(x - a)(x - b)}}{{(x - c)}}$ will assume all real values, provided