Question

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

x^2 - 6x + 9 = 0

a. Are the roots equal or unequal?
b. Are the roots rational or irrational?
c. Are the roots real or non-real?

(Please explain how you got the answers)​

Answer 1

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.