Question

In the equation above, c is a constant. If the equation has infinitely many solutions, what is the value of c ?

Hint:

**Hint:**

Infinitely many solutions of an equation means that the equation is true for any value of the variable. In other words, when we put any value of x in the equation, we get a statement which is always true, (example 0 =0 ). Here, to find the value of c, we simplify the given equation. As the equation is true for every value of x, we put x=1 to find the value of c.

* *

## The correct answer is:

### The given equation is

Expanding the terms of the above equation, we get

Simplifying the equation,

It is given that this equation has infinitely many solutions, so it must be true for all values of x.

We cannot put x=0 in the equation because then both the right hand side and the left hand side will be 0 and the term containing c will vanish.

Particularly, the above equation is true for x = 1

So,

Thus, we get that for , equation has infinitely many solutions.

The correct option is B)

**Note: **

As the equation is true for all values of x, we could have put x equal to any other number instead of 1, and we would get the same result. If we put x=1 in the first step as well, we would get the same value for x

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