Zeroes of a Quadratic Polynomial and Roots of a Quadratic Equation
The zeroes of a quadratic polynomial ax^2 + bx + c are the values of x for which the polynomial equals zero. These are the points where the graph of the quadratic polynomial intersects the x-axis.

Relationship between Zeroes and Roots
The zeroes of a quadratic polynomial are directly related to the roots of the corresponding quadratic equation ax^2 + bx + c = 0. The roots of a quadratic equation are the values of x for which the equation equals zero. In other words, the roots of the equation are the values of x that make the corresponding polynomial equal to zero.

Connection between Zeroes and Roots
- The zeroes of a quadratic polynomial are the x-intercepts of the graph of the polynomial, while the roots of the quadratic equation are the values of x that satisfy the equation.
- If α and β are the zeroes of the quadratic polynomial ax^2 + bx + c, then the roots of the quadratic equation ax^2 + bx + c = 0 are x = α and x = β.
- The relationship between the zeroes of a polynomial and the roots of the corresponding equation helps us in solving quadratic equations and understanding the behavior of quadratic functions.
In conclusion, the zeroes of a quadratic polynomial and the roots of the quadratic equation are closely connected, as they represent the points where the polynomial or equation equals zero. Understanding this relationship is crucial in solving quadratic equations and analyzing quadratic functions.