Question

Factorise the polynomial () = 20

2 − 9 + 1 and find the zeros​

Answer 1

Explanation:

Given polynomial, f(x) = 20x² - 9x + 1

⇒ f(x) = 20x² - (5 + 4)x + 1

⇒ f(x) = 20x² - 5x - 4x + 1

⇒ f(x) = 5x (4x - 1) - 1 (4x - 1)

⇒ f(x) = (4x - 1) (5x - 1)

This is the required factorization.

In order to find the zeros, we take f(x) = 0

⇒ (4x - 1) (5x - 1) = 0

∴ either 4x - 1 = 0 or 5x - 1 = 0

⇒ either 4x = 1 or 5x = 1

⇒ either x = 1/4 or x = 1/5

∴ the zeros of f(x) are 1/4 and 1/5