3bouquets of flowers are ordered at the florist. 3 roses 2 carnations and 1 tulip costs $14, 2 carnations and 6 tulips costs $38, and 1 rose 12 carnations and 1 tulip costs $18. how much does each item costs?

The correct answer is : Rose cost is 2.1$,

                                       carnation cost is 0.82$ and

                                        tulip cost is 6.06$

Solution:-

Let rose cost be r$, carnation cost be c$ and tulip cost be t$.

Given 3 roses,2 carnations and 1 tulip costs 14$.

That is 3r+2c+t = 14, let it be first equation.

Also given 2 carnations and 6 tulips costs 38$.

That is 2c+6t=38

           c+3t=19

            c=19-3t

Also 1 rose, 12 carnations and 1 tulip costs 18$.

That is r+12c+t=18

Let us plugin c=19-3t in above equation.

           r+12(19-3t)+t = 18

            r=35t-210

Let us plugin r and c in first equation.

3(35t-210)+2(19-3t)+t =14

105t-630+38-6t+t =14

100t = 606

  t=6.06$

c=19-3*6.06 = 0.82$

r=35*6.06-210=2.1$

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.