Question

factorize
4x² - 1400 + 60,000=0​

Answer 1

Answer:

4x² + 4bx - (a² - b²) = 0

4x² + 2 (a + b)x - 2 (a - b)x - (a² - b²)

[2(a - b) × 2 (a + b) = 4(a² - b²) & 2 (a - b) - 2 (a + b) = 4b]

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

[(a² - b²) = (a + b) (a - b) ]

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

x = - (a + b)/2 or x = (a - b)/2

Hence, the roots of the quadratic equation 4x² + 4bx - (a² - b²) = 0 are - (a + b)/2 & x = (a - b)/2