Consider the quadratic polynomial P(x)=x2−5x+6. Answer the following questions.
a. (i) Define a zero (or root) of a polynomial.
b. (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.
c. (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.