Question

If the graph of the quadratic polynomial does not intersect the x-axis at any point, then what can be said about the zeroes of the polynomial?​

Answer 1

Answer:

The graph of a polynomial of odd degree always crosses the x-axis, which means it has a zero.

It may easily happen that the graph of a polynomial of even degree does not intersect the x-axis.

In any case, for any function p, and a given value a, if p(a)=0, then by definition a is a zero of p and (a,0) is a point on the graph of p, and therefore p intersects the x-axis at a.

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