Which line is parallel to the line that passes through the points
(2, –5) and (–4, 1)?

Slope of  line that passes through two points:  

(2, -5)    ⇒    x₁ = 2,  y₁ = -5

(-4, 1)      ⇒   x₂ = -4,  y₂ = 1

Any line with a slope of -1 is parallel the line that passes through the points

(2, –5) and (–4, 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.