What are the factors of x² - 100 = 0?

Solution:

Given:

Quadratic equation is x² - 100 = 0 with degree 2.

As we know that the standard form of the quadratic equation is ax² + bx + c = 0 --- (1)

So comparing the given equation with the equation (1) we get,

a = 1, b = 0, c = 100

Now solving the quadratic equation by factorising

⇒ x² - 100 = 0

For factorising first split the middle term 0 as -10x and 10x as

-10x + 10x = 0 and (-10x) (10x) = -100x²

⇒ x² - 10x + 10x -100 = 0

⇒ x(x - 10) + 10(x - 10) = 0

⇒ (x + 10)(x - 10) = 0

We can understand by the given example:

Example:

What is the factors of n² - 25 = 0?

Given:

Equation is n² - 25 = 0

By solving we get,

⇒ n² = 25

⇒ √n² = √(25) (Applying square root both sides)

⇒ n = √(5)(5)

⇒ n = ±5

⇒ n = 5 and n = -5

⇒ The factors are (n - 5) and (n + 5)

---

What are the factors of x² - 100 = 0?

Summary:

By solving the given quadratic equation x² - 100 with factorising method we get the two linear factors as (x + 10) and (x - 10).