Number of zeroes of a polynomial
A polynomial function is a function that can be expressed in the form p(x) = a_n*x^n + a_{n-1}*x^{n-1} + ... + a_1*x + a_0, where a_n, a_{n-1}, ..., a_1, a_0 are constants and n is a non-negative integer.

Intersections and Touch Points
When a polynomial p(x) intersects the x-axis, it means that the value of p(x) is equal to zero at those points. Therefore, each intersection with the x-axis represents a zero of the polynomial.
If a polynomial touches the x-axis without crossing it, it means that the polynomial has a double root at that point. In other words, that particular x-value is a zero of multiplicity two.

Number of zeroes
When a polynomial intersects the x-axis twice, it means that there are two distinct zeros formed at those points. Additionally, when the polynomial touches the x-axis four times, it implies that there are two double roots (multiplicity two) formed at those points.
Therefore, the total number of zeroes formed by the polynomial in this scenario is four. Two distinct zeroes from the intersections and two double roots from the touch points.