For the given statements identify the sufficient condition
p·: If discriminarit of a quadratic equation is not a perfect square then its roots are irrational

Options

A. Roots are irrational
B. Discriminant is a perfect square
C. Discriminant is not a perfect square
D. Roots are rational

Answer

To determine the sufficient condition from the given statement, we can break down the reasoning step by step.

### Step-by-Step Solution:

1. **Understanding the Statement**: The statement provided is: "If the discriminant of a quadratic equation is not a perfect square, then its roots are irrational." This can be expressed in a logical format: If \( p \), then \( q \).

2. **Identifying \( p \) and \( q \)**:
- Let \( p \) be the statement: "The discriminant of a quadratic equation is not a perfect square."
- Let \( q \) be the statement: "The roots of the quadratic equation are irrational."

3. **Identifying Sufficient and Necessary Conditions**:
- In the logical implication "If \( p \), then \( q \)", the statement \( p \) is a sufficient condition for \( q \). This means that if \( p \) is true (the discriminant is not a perfect square), then \( q \) must also be true (the roots are irrational).
- The statement \( q \) is a necessary condition for \( p \). This means that for \( p \) to be true, \( q \) must also be true.

4. **Conclusion**: From the analysis, we conclude that the sufficient condition is \( p \), which is "The discriminant of a quadratic equation is not a perfect square."

### Final Answer:
The sufficient condition is: **The discriminant of a quadratic equation is not a perfect square.**

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