1. Now consider equations of the form , where a, b, and c are all positive integers and . (a) Create an equation of this form that has 7 as a solution and an extraneous solution. Give the extraneous solution. (b) What must be true about the value of to ensure that there is a real number solution to the equation? Explain.

a) To create an equation

X+X =7

so what's X over here is

7² = x²

X=3.5

b) Real numbers are mixture of irrational and rational numbers so √5 and √6 are irrational where as 5 and 6 are not but they two are equal to each other.

Explaining the equation:

√5 +√6 = √11

5 +6 = 11

√11 =11

√= 11 ÷ 11

√= 1

So if root is 1 then -1 is -√

this is the answer propably

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.

table 3 represents a direct variation function. : )