Recall the discussion on all the strange ideas for what could be done to both sides of an equation. let’s explore some of the same issues here but with inequalities. recall, in this lesson, we have established that adding (or subtracting) and multiplying through by positive quantities does not change the solution set of an inequality. we’ve made no comment about other operations.
a. squaring: do ≤6 and ²≤36 have the same solution set? if not, give an example of a number that is in one solution set but not the other.

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.

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,