Question

Find the roots of the following quadratic equation by the factorization method :

4x2 − 4ax + (a2 − b2) = 0​

Answer 1

Answer:

x = a + b/2, a - b/2

Step-by-step explanation:

4x² - 4ax + (a² - b²) = 0

⇒ 4x² - 4ax + (a² - b²) = 0

⇒ 4x² - [2(a + b)x - 2(a - b)]x + (a + b) (a - b) = 0

⇒ 4x² - 2(a + b)x - 2(a - b)x + (a + b) (a - b) = 0

⇒ [4x² - 2(a + b)x] - [2(a - b)x - (a + b) (a - b)] = 0

⇒ 2x[2x - (a + b)] - (a - b) [2x - (a - b)] = 0

⇒ [2x - (a + b)] [2x - (a - b)] = 0

⇒ [2x - (a + b)] = 0 or [2x - (a - b)] = 0

⇒ 2x = a + b or 2x = a - b

⇒ x = a + b/2, a - b/2

Hence, x = a + b/2, a - b/2

Hope it helps!