$A$ two-digit number is four times the sum of its digits and three times the product of its digits. The number is:

If $a, b, c$ are real numbers, then both the roots of the equation $(x-b)(x-c)+(x-c)(x-a)+(x-a)(x-b)=0$ are always

Consider the curves given by the following quadratic functions:

$f_1(x) = 5 x^2 + 2 x + 1$	$f_2(x) = 5 x^2 + 6 x + 1$
$f_3(x) = x^2 - 7 x + 6$	$f_4(x) = 64 x^2 + 48 x + 9$

If $A_1, A_2, A_3$ and $A_4$ denote the lengths of the intercepts on the $X$-axis made by the above curves respectively,then which of the following is true?

If the equation $x^2-3ax+a^2-2a-K=0$ has different real roots for every rational number $a$,then $K$ lies in the interval

If $\alpha$ and $\beta$ are the roots of the equation $x^2 - 3x + 1 = 0$,then what is the equation whose roots are $\frac{1}{\alpha - 2}$ and $\frac{1}{\beta - 2}$?

What are the roots of the equation $x^{2/3} + x^{1/3} - 2 = 0$?