Geometrical Meaning of Zeroes of a Polynomial

The video tutorial explains how to find the zeros of polynomials using graphs. It starts with linear polynomials, showing how to plot them and identify zeros where the graph intersects the X-axis. The tutorial then moves to quadratic polynomials, illustrating the U-shaped parabola and its zeros. Finally, it covers cubic polynomials, describing their S-shaped graphs and zeros. The video concludes with an analysis of various polynomial graphs, emphasizing the relationship between graph shapes and the number of zeros.

What is the primary purpose of a graph in mathematics?

• To calculate area

• To solve algebraic equations

• To display the relationship between two variables

• To measure angles

How do you determine the zero of a linear polynomial graphically?

• By finding where the graph intersects the Y-axis

• By finding where the graph intersects the X-axis

• By identifying the highest point on the graph

• By calculating the slope of the graph

What shape does the graph of a quadratic polynomial typically form?

• An ellipse

• A straight line

• A circle

• A parabola

How many zeros can a quadratic polynomial have?

• One or two

• Two or three

• Only one

• None

What is the shape of a cubic polynomial graph?

• A circle

• A straight line

• A parabola

• A sigmoidal shape

How many zeros can a cubic polynomial have?

• Two

• One

• Three

• Four

What can be inferred if a polynomial graph does not touch the X-axis?

• The polynomial has no zeros

• The polynomial has one zero

• The polynomial has infinite zeros

• The polynomial has two zeros