If a certain number is added to 24, the result is the same as if the number were multiplied by 3. what is the number?

The answer is the number 12. This is because if 12 is added to 24 it equals 36 and if 12 is multipled by 3 it is 36.

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.

she will travel a distance in the range of 3 - 11 miles