Hank says “I am thinking of a whole number N, and the clue is: Card 1
3N is a number less than 3.

Card 2
3N is an even number.

Card 3
3N is a square number.

Card 4
3N is a prime number.

Card 5
3N is a composite number.

Card 6
3N is a multiple of 3 and a multiple of 2.

Card 7
3N is factor of 36 and a factor of 18.

Card 8
Make up another card for Hank’s game. Include the answer.

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.