Which of the following sets of numbers could be the lengths of the sides of a triangle?
a. 7.4 cm, 10.5 cm, 15.5 cm
b. 10.5 cm, 15.5 cm, 4.5 cm
c. 7.4 cm, 15.5 cm, 23 cm
d. 7.4 cm, 10.5 cm, 19.5 cm

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.

40 x 50 = 2000

step-by-step explanation: