The smallest positive integral value of $a$, for which all the roots of $x^4 - ax^2 + 9 = 0$ are real and distinct, is equal to

If the expression $x^3+3x^2-9x+\lambda$ is of the form $(x-\alpha)^2(x-\beta)$,then the values of $\lambda$ are

If $1$ is a multiple root of order $3$ for the equation $x^4-2x^3+2x-1=0$,then the other root is

The positive root of $x^{2}-78.8=0$ after the first approximation by the Newton-Raphson method,assuming the initial approximation to the root is $14$,is:

Let $p(x) = x^2 + ax + b$ have two distinct real roots,where $a, b$ are real numbers. Define $g(x) = p(x^3)$ for all real numbers $x$. Then,which of the following statements are true?
$I.$ $g$ has exactly two distinct real roots.
$II.$ $g$ can have more than two distinct real roots.
$III.$ There exists a real number $\alpha$ such that $g(x) \geq \alpha$ for all real $x$.

The difference between the roots of the equation $x^2 + 2x + 4 = 0$ is ... (where $i = \sqrt{-1}$)