Do these ratios make a proportion? 3/20 and 10/61

Let's take a look at these numbers, and find out how they are or are not able to relate.

Let's look at the two numerators, 3 and 10. To get 3 to equal 10, you must multiply it by 3.333..repeated (you can find this by using 10/3).

Now, the two denominators, 20 and 61. In order to get 20 to 61, you must multiply it by 3.05 (61/20). Since 3.05 and 3.333 are not the same, the two numbers 3/20 and 10/61 are not proportional.

Another, easier way to find this is to simply divide the two numbers.

3/20=0.15

10/61=0.164

Again, since they are not the same, they are not proportional.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.