In the diagram, ∠AP B = 12◦ . Points Q, R, S, T, . . . alternate from one arm of
the angle to the other, each point located farther away from P than the point
before and P Q = QR = RS = ST = . . .. Eventually, one of the isosceles
triangles will be an equilateral triangle. How many isosceles triangles will be
formed before the equilateral triangle is formed?

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.

step-by-step explanation:

x = 3 ± √(5+y)