Question
Question: If the equation x<sup>2</sup> – (2 + m) x + (m<sup>2</sup> – 4m + 4) = 0 has coincident roots, then-...
If the equation x2 – (2 + m) x + (m2 – 4m + 4) = 0 has coincident roots, then-
A
m = 0, m = 1
B
m = 0, m = 2
C
m = 2/3, m = 6
D
m = 2/3, m = 1
Answer
m = 2/3, m = 6
Explanation
Solution
Since roots are coincident, we have
(–(2 + m))2 – 4.1. (m2 – 4m + 4) = 0
⇒ 4 + m2 + 4m – 4m2 + 16m – 16 = 0
⇒ 3m2 – 20m + 12 = 0 ⇒ m = 2/3, 6.