Let $a_n, a_{n-1}, \ldots, a_1, a_0 \in \mathbb{C}$ and $f(x) = a_n x^n + a_{n-1} x^{n-1} + \ldots + a_1 x + a_0$ be a polynomial. If the polynomial $f(x)$ is monic,then:

Solve the equation $x^{2}+\frac{x}{\sqrt{2}}+1=0$.

The equation $16x^4 + 16x^3 - 4x - 1 = 0$ has a multiple root. If $\alpha, \beta, \gamma, \delta$ are the roots of this equation,then $\frac{1}{\alpha^4} + \frac{1}{\beta^4} + \frac{1}{\gamma^4} + \frac{1}{\delta^4} =$

The equation $\sqrt{x + 1} - \sqrt{x - 1} = \sqrt{4x - 1}$ for $x \in R$ has:

The graph of $y = ax^2 + bx + c$ is shown. Which of the following does $NOT$ hold good?

If $P(x)=ax^{2}+bx+c$ and $Q(x)=-ax^{2}+dx+c$, where $ac \neq 0$ ($a, b, c, d$ are all real), then $P(x) \cdot Q(x)=0$ has