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.
