If $AM$ and $GM$ of roots of a quadratic equation are $5$ and $4$,respectively,then the quadratic equation is

The number of non-real roots of the equation $x^{10}-3x^8+5x^6-5x^4+3x^2-1=0$ is

If $k \in R$ is such that the equation $2 \cosh^2 x = 3 \sinh x + k$ has no real solution,then which of the following is correct?

Let $p, q \in \mathbb{Q}$. If $2 - \sqrt{3}$ is a root of the quadratic equation $x^2 + px + q = 0$,then:

Let $\alpha, \beta$ be two roots of the quadratic equation $x^2+ax-b=0, b \neq 0$. If the straight line $x \cos \theta + y \sin \theta = c$ touches the curve $(\frac{x}{\alpha})^n + (\frac{y}{\beta})^n = 2$ at the point $(\alpha, \beta)$, then $(\frac{a}{b})^2 + \frac{2}{b} =$

The value of $m$ for which the equation $\frac{a}{x + a + m} + \frac{b}{x + b + m} = 1$ has roots equal in magnitude but opposite in sign is