CBSE Class 10 Answered

Geometrical Interpretation of zeros

It is possible to find the zeros of any polynomial p(x) by just drawing its graph and identifying the points where its graph meets x-axis. The points at which the graph of a polynomial meets x axis are its zeros.

• The number of real zeros of the polynomial is the number of times its graph intersects x axis. A polynomial p(x) of degree n will intersect the x-axis at atmost n points.
  
  
• Points where the graph of polynomial touch the x-axis is also the zero of the polynomial.

• A linear polynomial has atmost one real zero.

• A quadratic polynomial has atmost two real zeros.

• A cubic polynomial has atmost three real zeros.