How many solutions would the equation (𝑥−3)(𝑥−3) = 0 have?

Question

A. One Solution

B. Two Solutions

C. No Solution

Explain your reasoning choosing ___ (A,B,or C)

How can you determine the number of solutions of the graph?

Answer 1

x=3 is the only solution

However, it's usually considered to be 3 with multiplicity 2

in other words, x = 3 and 3, 2 solutions, although they're both the same

the number of solutions = the degree of the equation

(x-3)(x-3) = x^2 -6x + 9 =0

the highest powered term tells you the degree x^2 has degree 2, which means 2 solutions, although they are both equal in this equation. x = 3, 3