The set of values of a for which 4 t - a -4 2 t -9 a -4-0 - t -1-2 isA- 1- a-48B- a 128-7C- -48 -128-7- -D- a -

The correct option is D Let 2^t =x then f(x) = x^2 (a 4) x +9a/4 F(x) lt; 0. "for every x ϵ (2^1, 2^2) One of the roots of f(x) must be less than 2 an ...

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Standard XI

Mathematics

Range

The set of va...

Question

The set of values of a for which $4^{t} - (a - 4) 2^{t} + \frac{9 a}{4}$ < 0 $\forall t ϵ (1, 2)$ is

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( , -48 )

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Solution

The correct option is D

Let $2^{t}$ =x then f(x) = $x^{2}$ - (a - 4) x + $\frac{9 a}{4}$

F(x) < 0. "for every x $ϵ$ ( $2^{1}, 2^{2}$ )

One of the roots of f(x) must be less than 2 and the other must be greater than 4

i.e. f(2) < 0and f(4) < 0

$\Rightarrow a ϵ ϕ$

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The set of values of a for which 4t−(a−4)2t+9a4 < 0 ∀ tϵ(1,2) is

The correct option is D Let 2t =x then f(x) = x2 - (a - 4) x +9a4 F(x) < 0. "for every x ϵ (21,22) One of the roots of f(x) must be less than 2 and the other must be greater than 4 i.e. f(2) < 0and f(4) < 0 ⇒aϵϕ

The set of values of a for which $4^{t} - (a - 4) 2^{t} + \frac{9 a}{4}$ < 0 $\forall t ϵ (1, 2)$ is

The correct option is D

Let $2^{t}$ =x then f(x) = $x^{2}$ - (a - 4) x + $\frac{9 a}{4}$

F(x) < 0. "for every x $ϵ$ ( $2^{1}, 2^{2}$ )

One of the roots of f(x) must be less than 2 and the other must be greater than 4

i.e. f(2) < 0and f(4) < 0

$\Rightarrow a ϵ ϕ$