Question

If the graph of \( y = p(x) \) does not intersect the X-axis at all, then the zeroes of \( p(x) \) are:

• A. are equal
• B. are unequal
• C. don't exist
• D. All of these

Hint:

If a polynomial's graph does not intersect the X-axis, then it has no real zeros. This occurs when the polynomial has complex roots or no real solutions.

Answer 1

The Correct Option is C

Step 1: Understand the meaning of the graph not intersecting the X-axis
If the graph of the polynomial \( y = p(x) \) does not intersect the X-axis, it means that there are no real roots or zeros of the polynomial. This happens when the polynomial has no real solutions. Step 2: Conclusion
Since the graph does not intersect the X-axis, there are no real zeros for \( p(x) \). Therefore, the zeroes do not exist. The correct option is \( (3) \).