Question

Solve the quadratic equation by completing the square x^2-2ax+b=0​

Answer 1

Let a, ß be the roots of x² + 2ax + b =0.......[1]

⇒a + ß = -2a and aß = b

By hypothesis

la-ß | ≤ 2m

⇒ (a-ß)² ≤ 4m²

⇒ (a+ß)²-4aß < 4m²

⇒ 4a²-4b ≤ 4m²

⇒a² - b ≤ m²......(2)

And discriminant of (1) is >0

⇒4a²-4b> 0

⇒ b <a²...... (3)

From (2) and (3)

a² > b≥ (a² - m²)

b = [a² - m², a²)