Question
Question: If the roots of the equation x<sup>2</sup> – 2ax + a<sup>2</sup> + a – 3 = 0 are less than 3 then...
If the roots of the equation x2 – 2ax + a2 + a – 3 = 0 are less than 3 then
A
a < 2
B
2 ≤ a ≤ 3
C
3 < a ≤ 4
D
a > 4
Answer
a < 2
Explanation
Solution
Since roots are less than a real number, roots must be real
⇒ 4a2 – 4(a2 + a – 3) ≥ 0 ⇒ a ≤ 3. … (1)
Let f(x) = x2 – 2ax + a2 + a – 3. Since 3 lie outside the roots,
f(3) > 0 ⇒ a < 2 or a > 3. . . . .(2)
From (1), (2) we have a < 2