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Step-by-step explanation:

1. 5(x+2) = 3(x+8)

  5x + 10 = 3x + 24

  2x + 10 = 24

  2x = 14

  x=7

2. 6(t-1) = 9(t-4)

   6t - 6 = 9t - 36

   -3t - 6 = -36

   -3t = -30

   t = 10

3. 4(w-6) = 3(w+1)

   4w - 24 = 3w + 3

   w - 24 = 3

   w = 27

4. 10b - 45 = 3(b-15)

   10b - 45 = 3b - 45

    7b - 45 = -45

    7b = 0

    b = 0

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.