Polynomials – Notes
Geometrical Meaning of the Zero Polynomial
The x-coordinate of the point, where the graph of a polynomial intersects the x-axis is called the zero of the polynomial.
An nth-degree polynomial intersects the x-axis at maximum of n points and therefore, has a maximum of n zeroes.
In a quadratic polynomial ax2 +bx + c,
- If a > 0, then the graph is a parabola that open upwards.
- If a < 0, then the graph is a parabola that open downwards.
Relationship between Zeros and Coefficients of a Polynomial
If a is the of a linear polynomial ax + b, then a =- = –
If a and b are the two zeroes of a quadratic polynomial ax2 + bx + c, then: