Consider the quadratic polynomial

MATHEMATICS · Multi-part · CBSE · Mathematics · Polynomials · Polynomials

Problem

P(x)=x^{2}-5x+6

. Answer the following questions. (i) Define a zero (or root) of a polynomial. (ii) A student claims that

x=2

is a zero of

P(x)

because

P(2)=0

. Explain, in words, why substituting a number into a polynomial and obtaining the value

0

confirms that the number is a zero. (iii) State the point on the Cartesian plane that corresponds to the zero

x=2

for the graph of

y=P(x)

and briefly justify your answer.