Question
Question: If roots of equation x<sup>2</sup> – 2ax + (a<sup>2</sup> + a – 3) = 0 are real and less than 3 the...
If roots of equation x2 – 2ax + (a2 + a – 3) = 0 are real and less
than 3 then
A
a < 2
B
2 £ a £ 3
C
3 < a £ 4
D
a > 4
Answer
a < 2
Explanation
Solution
(1) D ³ 0
(2) f(3) > 0
(3) –2ab < 3 
(1) 4a2 – 4.(a2 + a – 3) ³ 0
a – 3 £ 0 Ž a £ 3
(2) 9 – 6a + a2 + a – 3 > 0
a2 – 5a + 6 > 0
Ž (a – 3) (a – 2) > 0
Ž a > 3, a < 2
(3) + 22a < 3 Ž a < 3
Common value of a