Question

# All possible values of $$a$$, so that $$6$$ lies between the roots of the equation $$x^2 + 2(a - 3)x + 9 = 0$$ is

A
(,2)(2,)
B
(,34)
C
(2,)
D
none of these

Solution

## The correct option is B $$\left(- \infty, -\dfrac{3}{4}\right)$$Given equation,$$x^2 + 2(a - 3)x + 9 = 0$$Condition for a number 6 to lie between the roots is $$f(6) < 0 \ldots\ldots (\because a.f(k)<0)$$$$\Rightarrow 36 + 12(a - 3) + 9 < 0$$$$\Rightarrow 12a + 9 < 0$$$$\Rightarrow a < \displaystyle -\frac{3}{4}$$  $$\displaystyle a \in \left( - \infty , - \frac{3}{4}\right)$$Mathematics

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