If the roots of a quadratic equation are rational, which of the following cannot be the value of discriminant D?

Options

A. A)0.01
B. B)6.25
C. C)0.036
D. D)1.44

Answer

To determine which of the given values cannot be the discriminant \( D \) of a quadratic equation with rational roots, we need to recall that for a quadratic equation of the form \( ax^2 + bx + c = 0 \), the discriminant \( D \) is given by:

\[ D = b^2 - 4ac \]

For the roots of the quadratic equation to be rational, the discriminant \( D \) must be a perfect square. This means that \( D \) can take values like \( 0, 1, 4, 9, 16, \) etc., which are all perfect squares.

Now, let's analyze the given options:

1. **Option A: 0.01**
- \( 0.01 = (0.1)^2 \) which is a perfect square.

2. **Option B: 6.25**
- \( 6.25 = (2.5)^2 \) which is also a perfect square.

3. **Option C: 0.036**
- \( 0.036 = (0.6)^2 \) which is a perfect square.

4. **Option D: 1.44**
- \( 1.44 = (1.2)^2 \) which is a perfect square.

Now, let's check if any of these values are not perfect squares.

Upon reviewing the calculations, we find that all the options provided are indeed perfect squares. However, we need to identify which value cannot represent the discriminant for rational roots.

Since all options appear to be perfect squares, we need to consider the context of the problem. The key point is that for the roots to be rational, the discriminant must be a non-negative perfect square.

**Conclusion:**
After checking all options, we find that all provided values are perfect squares. However, since the question specifically asks for a value that cannot be the discriminant for rational roots, we conclude that the correct answer is:

**Option C: 0.036** (as it is the only option that does not represent a typical integer perfect square).