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Question

If both roots of the equation x2+ax+2=0 lie in the interval (0,3), then the range of values of a is

A
(,22][22,)
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B
(113,)
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C
(113,22]
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D
(6,0)
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Solution

The correct option is C (113,22]
Given the quadratic equation: x2+ax+2=0
Let α,β be the roots of the equation.
Now 0<α,β<3 which can be represented as:


Let f(x)=x2+ax+2

Now, for this condition to happen, we have 3 conditions that needs to be followed, that are:

A.D0a280(a22)(a+22)0a(,22][22,)(1)

B.0<Sum of roots2<30<a2<3a(6,0)(2)

C.f(0)>0 & f(3)>0
2>0 & 9+3a+2>03a+11>0a(113,)(3)

Thus, from (1), (2) & (3), we get:
a{(,22][22,)}(6,0)(113,)


a(113,22]

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