Question
Question: If the roots of the equation x<sup>2</sup> + a<sup>2</sup> = 8x + 6a be real then the set of values ...
If the roots of the equation x2 + a2 = 8x + 6a be real then the set of values of a is
A
[–1, 7]
B
(–2, 8)
C
[–2, 8]
D
None of these
Answer
–2,8
Explanation
Solution
x2 + a2 –8x – 69 = 0
x Ī R so B2 – 4AC = +ve
so 4(16 + 6a –a2) = –4(a + 2) (a – 8) = +ve
Ž (a + 2) (a – 8) is –ve
[–2, 8]