Question
Question: The value of ‘a’ so that the sum of the squares of the roots of the equation x<sup>2</sup> – (a – 2)...
The value of ‘a’ so that the sum of the squares of the roots of the equation x2 – (a – 2) x – a + 1 = 0. assume the least value, is
A
2
B
0
C
3
D
1
Answer
1
Explanation
Solution
x2 – (a – 2) x – a + 1 = 0
a + b = (a – 2), ab = 1 – a
a2 + b2 = (a + b)2 – 2ab = (a – 2)2 – 2 (1 – a)
= a2 – 4a + 4 – 2 + 2a = a2 – 2a + 2
= (a – 1)2 + 1
It is minimum when a = 1