Question

Solve the following equations by using the Quadratic formula and answer the subsequent questions:

Answer 1

Answer:

Step-by-step explanation:

Note that x^2 - 6x + 9 = 0 can be rewritten as the square of a binomial:

(x - 3)^2

and the roots are found by setting this equal to zero and solving for x:

(x - 3)^2 = 0, or x - 3 = ±0, or x = 3 and x = 3

a) there are two equal roots:  {3, 3}

b) the roots {3, 3} are rational

c) the roots {3, 3) are real

If you want to use the quadratic formula, proceed as follows:

1.  Identify the coefficients of the quadratic:  {1, -6, 9}

2. Find the discriminant b^2 - 4ac:  It is (-6)^2 - 4(1)(9) = 36 = 36 = 0

   As a general rule, if the discriminant is zero, the quadratic has two equal, real roots.  These roots are rational:  3 can be rewritten as 3/1, which is a ratio.