If x² - 6x + 8 = 0, then x - 4 = 0 or x - 2 = 0. State True or False.

Quadratic equations are those equations that have a degree equal to two. They have many applications in various fields of engineering and science.

Answer: It is true that, if x² - 6x + 8 = 0, then x - 4 = 0 or x - 2 = 0.

Let's understand why.

Explanation:

Given equation: x² - 6x + 8 = 0

Now, we will use splitting the middle term method to find the solution to the problem.

⇒ x² - 6x + 8 = 0

⇒ x² - 4x - 2x + 8 = 0

⇒ x(x - 4) - 2(x - 4) = 0

⇒ (x - 2)(x - 4) = 0

Now, either x - 2, or x - 4 = 0.

Thus, x = 2 and x = 4 are the roots of the equation.

We can also find the same solution using the discriminant formula. 

Hence, it is true that, if x² - 6x + 8 = 0, then x - 4 = 0 or x - 2 = 0.