ZEROS OF POLYNOMIAL

GEOMETRIC  MEANING OF ZEROS OF POLYNOMIAL

The zero of the polynomial is defined as any real value of x, for which the value of the polynomial becomes zero.

A real number k  is a zero of a polynomial p(x), if .p(k) =0

Geometrical Meaning of the Zeroes of a Polynomial: The zero of the polynomial is the x-coordinate of the point, where the graph intersects the x-axis. If a polynomial p(x)  intersects the x-axis at (k,0) , then k  is the zero of the polynomial.

The graph of a linear polynomial intersects the x-axis at a maximum of one point. Therefore, a linear polynomial has a maximum of one zero.

The graph of a quadratic polynomial intersects the x-axis at a maximum of two points. Therefore, a quadratic polynomial can have a maximum of two zeroes. In case of a quadratic polynomial, the shape of the graph is a parabola. The shape of the parabola of a quadratic polynomial ax² +bx +c , a≠ 0  depends on ‘a’ .

If  a> 0 , then the parabola opens upwards.

If a < 0 , then the parabola opens downwards.

The graph of a cubic polynomial intersects the x-axis at maximum of three points. A cubic polynomial has a maximum of three zeroes. In general, an nth-degree polynomial intersects the x-axis at a maximum of n points. Therefore, an nth-degree polynomial has a maximum of n zeroes.