NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 4: Quadatric Equation - Exercise 4.2

Question 3

Let us check step by step:

1. A quadratic equation is of the form \(ax^2 + bx + c = 0\), where \(a, b, c\) are numbers and \(a \neq 0\).
2. "Integral coefficients" means that \(a, b, c\) are whole numbers (positive, negative, or zero).
3. The statement says: "If the coefficients are integers, then the roots must also be integers."
4. To check this, we try an example: \(x^2 - 2 = 0\).
5. Here, \(a = 1, b = 0, c = -2\). All are integers, so coefficients are integral.
6. Now solve it: \(x^2 - 2 = 0 \implies x^2 = 2 \implies x = \pm \sqrt{2}\).
7. But \(\sqrt{2}\) is not an integer (it is an irrational number).
8. This shows that even if the coefficients are integers, the roots may not be integers.

Therefore, the statement is false.