If the roots of $x^4-10x^3+37x^2-60x+36=0$ are $\alpha, \alpha, \beta, \beta$ with $\alpha < \beta$,then find the value of $2\alpha+3\beta-2\alpha\beta$.

If $\alpha$ is a root of multiplicity $3$ of the equation $x^5-8x^4+25x^3-38x^2+28x-8=0$,then $\alpha^2-5\alpha+6=$

If one root of the quadratic equation $x^2 + px + (1 - p) = 0$ is $(1 - p)$,then what are its roots?

Solve the equation $x^{2}-2x+\frac{3}{2}=0$.

The value of $k$ for which the quadratic equation $kx^2 + 1 = kx + 3x - 11x^2$ has real and equal roots is:

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?