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Question

If both the roots of x2+2ax+a=0 are less than 2, then the set values of a is

A
[45,0)(1,)
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B
(,0][1,)
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C
(45,0][1,)
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D
(2,0][1,)
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Solution

The correct option is C (45,0][1,)
Let f(x)=x2+2ax+a, whose roots are α,β
Given: α,β<2


Conditions:
(i) Δ04a24a0
a(a1)0a0 or a1 (1)

(ii) B2A<22a2<2a>2 (2)

(iii) f(2)>05a+4>0a>45 (3)

From (1),(2) and (3), we get
a(45,0][1,)

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