Question

Find the zeroes of the polynomial.
P(x) = x2-4.

Answer 1

P ( x ) = x² - 4

We can also write this as :

⇒ P ( x ) = (x)² - (2)²

Identity : a² - b² = (a + b)(a - b)

⇒ P ( x ) = (x + 2)(x - 2)

To find the zeroes, P ( x ) = 0

•°• 0 = (x + 2)(x - 2)

Using Zero Product Rule

⇒ (x + 2) = 0 and (x - 2) = 0

⇒ x = - 2 and x = 2

Hence, the zeroes are 2 and - 2.

Answer 2

Given:

P(x) = x²-4

To Find:

the zeros of the polynomial

Solution:

The given equation P(x) = x²- 4 can also be written as,

P(x) = (x)² - (2)²

Now, by using a² - b² = (a + b)(a - b)

⇒ P(x) = (x+2)(x-2)

Now to find the values of P(x) = 0

⇒ 0 = (x + 2)(x - 2)

⇒ (x + 2) = 0 and (x - 2) = 0   [using the zero product rule]

⇒ x = -2 and x = 2

Therefore, the zeroes of the polynomial are 2 and -2.