The angles of elevation of the top of a cliff from two boats A and B on the same side of the cliff and on the same horizontal level with the foot of the cliff are 30°
and 50° respectively. If the distance from the foot of the cliff to boat B is 30 m,
find by scale drawing:
(a) the height of the cliff.
(b) the distance between A and B.​

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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.