# The zeroes of a polynomial are the solutions of the equations p(x)=0, whereP(x) represents the polynomial. If we graph

The zeroes of a polynomial are the solutions of the equations p(x)=0, where
P(x) represents the polynomial. If we graph the polynomial say=p(x) then we
Find these are the values of x where y=0.Hence zeroes of the polynomial are
x-intercepts of the graph

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P R E C A L C U L U S

7

THE ROOTS, OR ZEROS,

OF A POLYNOMIAL

The polynomial equation

The roots, or zeros, of a polynomial

The x- and y-intercepts

IN THIS TOPIC we will present the basics of drawing a graph.

1.  What is a polynomial equation?

It is a polynomial set equal to 0.  P(x) = 0.

P(x) = 5×3 − 4×2 + 7x − 8 = 0

2.  What do we mean by a root, or zero, of a polynomial?

It is a solution to the polynomial equation, P(x) = 0.

It is that value of x that makes the polynomial equal to 0.

In other words, the number r is a root of a polynomial P(x)

if and only if  P(r) = 0.

Example 1.   Let P(x) = 5×3 − 4×2 + 7x − 8.  Then a root of that polynomial is 1 because, according to the definition:

P(1) = 5· 13 − 4· 12 + 7· 1 − 8   = 5 − 4 + 7 − 8   = 0.

It is traditional to speak of a root of a polynomial.  Of a function in general, we speak of a zero.

Example 2.   The roots of this quadratic

x2 −x − 6 = (x + 2)(x − 3)

are −2 and 3.  Those are the values of x that will make the polynomial equal to 0.

3.  What are the x-intercept and y-intercept of a graph?

The x-intercept is that value of x where the graph crosses or touches the x-axis.  At the x-intercept — on the x-axis — y = 0.

The y-intercept