Which of the following equations has infinitely many real solutions? a. 3(x - 7) = 3x + 21 b. 3x + 1 = 3x - 1 c. 3x + 1 = x - 1 d. 3(x - 7) = 3x - 21

Answer is D. 3(x - 7) = 3x - 21

because

3(x - 7) = 3x - 21

Distributive property

3x - 21 = 3x - 21

0 = 0

Infinitely many real solutions

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.