Question

True or false, an equation with an integer coefficient will always have an integer solution.

Answer 1

False wanna know why?

x^2 - 2 = 2

has integer coefficients
but the solutions are not integers

Answer 2

The statement is false.

Explanation:

Consider the provided statement.

An equation with an integer coefficient will always have an integer solution.

Let's understand this with the help of an example:

`x^2-3=0`

Here the coefficient of x is an integer.

Now find the solution as shown.

`x^2=3`

`x=\pm √(3)`

Hence the solution for the equation is ±√3.

As we know √3 is an irrational number and it is not an integer,

Therefore, the above statement is false.