Answer:

To understand why the statement is true, let's first revisit the concept of zeros of a quadratic polynomial and the graph of a quadratic function.

Quadratic Polynomial:
A quadratic polynomial is a polynomial of degree 2, written in the form ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Zeros of a Quadratic Polynomial:
The zeros (also known as roots or x-intercepts) of a quadratic polynomial are the values of x for which the polynomial equals zero. In other words, the zeros are the x-values at which the graph of the quadratic polynomial intersects the x-axis.

Graph of a Quadratic Polynomial:
The graph of a quadratic polynomial is a parabola. Depending on the coefficients, the parabola can open upwards (concave up) or downwards (concave down). If the parabola intersects the x-axis at two distinct points, the zeros are real and unequal. If the parabola is tangent to the x-axis at only one point, the zeros are equal and real.

Explanation of the Statement:
The given statement states that the graph of a quadratic polynomial cuts the x-axis at only one point. This means that the parabola representing the quadratic polynomial is tangent to the x-axis at a single point. In this case, the parabola does not intersect the x-axis at any other point. Therefore, there is only one value of x for which the quadratic polynomial equals zero, which implies that the zeros of the quadratic polynomial are equal and real.

Conclusion:
Based on the explanation above, we can conclude that the statement is true. When the graph of a quadratic polynomial cuts the x-axis at only one point, the zeros of the quadratic polynomial are equal and real.