Rewrite the following statements in if then form a) catching the 8: 05 bus is a sufficient condition for my being on time for work b) being divisible by 3 is a necessary condition for this number to be divisible by 9 o) the cubs will win the pennant only if they win tomorrow's game.

a. If I Catch the 8:05 bus, then I will arrive on time for work.

b. If an integer is divisible by 9, then that integer is divisible by 3.

C. If the Cubs win tomorrow's game, then they win the pennant and if the Cubs have won the pennant it is because they will have won the game tomorrow.

Step-by-step explanation:

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.