Question

The quadratic equation x2 – 6x + 9 = 0 has two distinct real roots.
true
false​

Answer 1

Answer: (x - 3)²

Explanation:

Let's factor the quadratic:

`\sf{x^2-6x+9=0}`

Think of two numbers that:

• multiply to 9
• add to -6

These numbers are -3 and -3.

The quadratic is therefore factored as:

(x - 3)(x - 3)

Now, the zeros of this function are:

x - 3 = 0 x - 3 = 0

x = 3 x = 3

Answer 2

false

Explanation:

x² - 6x + 9 = 0

consider the factors of the constant term (+ 9) which sum to give the coefficient of the x- term (- 6)

the factors are - 3 and - 3, since

- 3 × - 3 = + 9 and - 3 - 3 = - 6

use these factors to split the x- term

x² - 3x - 3x + 9 = 0 ( factor the first/second and third/fourth terms )

x(x - 3) - 3(x - 3) = 0 ← factor out common factor (x - 3) from each term

(x - 3)(x - 3) = 0

equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 3 = 0 ⇒ x = 3

thus the equation has 2 real and equal roots