Question
Question: If the roots of the equation x<sup>2</sup> – 2ax + a<sup>2</sup> + a – 3 = 0 are real less than 3, t...
If the roots of the equation x2 – 2ax + a2 + a – 3 = 0 are real less than 3, then
A
a< 2
B
2 ≤ a ≤ 3
C
3 < a ≤ 4
D
a > 4
Answer
a< 2
Explanation
Solution
s
f (x) = x2 – 2ax + a2 + a – 3 = 0, f (3) > 0, α + β < 6,
∆ ≥ 0.
⇒ a2 – 5a + 6 > 0, a < 3, - 4a + 12 > 0 ⇒ a < 2 or a > 3, a < 3,
a < 3 ⇒ a < 2