Question
Question: If *x*<sup>2</sup> – (a – 3) *x* + a = 0 has at least one positive root, then –...
If x2 – (a – 3) x + a = 0 has at least one positive root, then –
A
a Ī (–, 0) Č [7, 9]
B
a Ī (–, 0) Č [7, )
C
a Ī (–, 0] Č [9, )
D
None of these
Answer
a Ī (–, 0] Č [9, )
Explanation
Solution
x2 – (a – 3) x + a = 0,
D = (a – 3)2 – 4a = a2 – 10a + 9
D ³ 0 Ž (a – 9) (a – 1) ³ 0
Ž a Ī (–, 1] Č [9, )
Case 1 : When both roots are positive
D ³ 0 Ž (a – 9) (a – 1) ³ 0
Ž D ³ 0, a > 0, a > 3 Ž a Ī [9, ) …(1)
Case 2 : When exactly one root is positive
Ž a £ 0 …(2)
Thus, from (1) and (2), a Ī (–, 0] Č [9, ).
Hence (3) is correct answer.