Find the value of a for which the solution of the inequality is all real numbers.
3x+8+2ax≥3ax−4a
how do i solve for a and what does a stand for m.

Step-by-step explanation:

In the inequality

a is an arbitrary real number.

Separate the terms with x into left side and the terms without x in the right side:

First, look at the leading coefficient at x. If this coefficient is equal to 0 (when ), then the inequality is

This is true inequality for all x, so at the inequality (1) has the solution

Now, if the leading coefficient

then we can divide the inequality (2) by this positive number and get

If the leading coefficient

then we can divide the inequality (2) by this negative number and get

So, the answer is

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.