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Question

The values of a for which the number 6 lies in between the roots of the equation x2+2(a3)x+9=0, belong to
  1. (34,)
  2. (,34)
  3. (,0)(6,)
  4. (,0)(3,)


Solution

The correct option is B (,34)

f(x)=x2+2(a3)x+9 is a parabola facing upwards as shown in the figure.
Let the roots be α and β with α<β
If 6 lies between α and β,
f(6)<0
(6)2+2(a3)(6)+9<0
12a+9<0
a<34

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