If $f(x) = ax^{2} + bx + 2$ and $f(1) = 4, f(3) = 38$,then $a - b = $

$4+\frac{1}{4+\frac{1}{4+\frac{1}{4+\ldots \infty}}} = $

If $a > 0$,then the value of $\sqrt{a + \sqrt{a + \sqrt{a + \dots \infty}}}$ is:

If the equation $a(b-c)x^2 + b(c-a)x + c(a-b) = 0$ has equal roots,where $a + c = 15$ and $b = \frac{36}{5}$,then $a^2 + c^2$ is equal to . . . . . .

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 the roots of the quadratic equation $ax^2+bx+c=0$ are imaginary,then for all real values of $x$,the minimum value of the expression $3a^2x^2+6abx+2b^2$ is