The number of solutions for the equation $x^2-5|x|+6=0$ is .........

If the roots of the equation $\frac{1}{x + p} + \frac{1}{x + q} = \frac{1}{r}$ are equal in magnitude but opposite in sign,then the product of the roots will be

Two positive distinct numbers $a$ and $b$ each differ from their reciprocal by $1$. The value of $a + b$ is

Let $a \neq 0$ and $p(x)$ be a polynomial of degree greater than $2$. If $p(x)$ leaves remainders $a$ and $-a$ when divided respectively by $x+a$ and $x-a$,then the remainder when $p(x)$ is divided by $x^2-a^2$ is:

If the roots of the equation $x^2 - 2cx + ab = 0$ are real and unequal,then the roots of the equation $x^2 - 2(a + b)x + a^2 + b^2 + 2c^2 = 0$ are

If $1+\sqrt{2}$ and $2-i$ are the roots of the equation $x^4+bx^3+cx^2+dx+e=0$ where $b, c, d, e$ are rational numbers,then the roots of the equation $bx^2+cx+d=0$ are