The equation $\frac{3}{x - a^3} + \frac{5}{x - a^5} + \frac{7}{x - a^7} = 0$,where $a > 1$,has:

If $a, b, c$ are distinct odd natural numbers, then the number of rational roots of the equation $ax^2 + bx + c = 0$ is:

If the roots of the given equation $(\cos p-1) x^2+(\cos p) x+\sin p=0$ are real,then

Let $\alpha, \beta$ be the roots of the equation $x^{2}-\sqrt{2}x+\sqrt{6}=0$ and $\frac{1}{\alpha^{2}}+1, \frac{1}{\beta^{2}}+1$ be the roots of the equation $x^{2}+ax+b=0$. Then the roots of the equation $x^{2}-(a+b-2)x+(a+b+2)=0$ are...

If $l, m, n$ are real and $l \neq m$,then the roots of the equation $(l - m)x^2 - 5(l + m)x - 2(l - m) = 0$ are

Let $[x]$ be the greatest integer less than or equal to $x$ for a real number $x$. Then the equation $[x^2] = x + 1$ has: