The number of real solutions of the equation $(\frac{3}{2})^x = -x^2 + 5x - 10$ is:

$Quantity \, 1$: Time taken by Manoj and Shubham to complete the work together. When Manoj works alone,he takes $4.8 \, \text{hrs}$ more than the time taken by Manoj and Shubham to complete the work together. When Shubham works alone,he takes $10.8 \, \text{hrs}$ more than the time taken by both of them to complete the work together.
$Quantity \, 2$: $7.4 \, \text{hrs}$.

If the sum of the roots of the quadratic equation $ax^2 + bx + c = 0$ is equal to the sum of the squares of their reciprocals,then $a/c, b/a, c/b$ are in

If $a - \frac{1}{a - 3} = 5$,then the value of $(a - 3)^{3} - \frac{1}{(a - 3)^{3}}$ is

The equation $\sqrt{3 x^{2}+x+5}=x-3$,where $x$ is real,has

If $p$ and $q$ are non-zero real numbers and $\alpha^3 + \beta^3 = -p$,$\alpha \beta = q$,then a quadratic equation whose roots are $\frac{\alpha^2}{\beta}$ and $\frac{\beta^2}{\alpha}$ is