Question

2.

The roots of the equation x2-3x - m(m + 3) = 0,
where m is a constant, are
(a) m, m + 3
(b) -m, m + 3
(c) m,- (m+3) (d) -m, -(m + 3)
(AI 2011)​

Answer 1

(b) -m, m + 3

Explanation:

x² − 3x − m(m + 3) = 0

x² − 3x = m(m + 3)

x² − 3x + 9/4 = m(m + 3) + 9/4

(x − 3/2)² = m(m + 3) + 9/4

(x − 3/2)² = m² + 3m + 9/4

(x − 3/2)² = (m + 3/2)²

x − 3/2 = ±(m + 3/2)

x − 3/2 = m + 3/2, -m − 3/2

x = m + 3, -m