If α, β be the roots of 4 x 2-16 x +λ=0, where λ ∈ R, such that 1

Question

If α, β be the roots of 4 x 2-16 x +λ=0, where λ ∈ R, such that 1< α< 2 and 2< β< 3, then the number of integral values of λ is (A) 5 (B) 6 (C) 2 (D) 3

Tardigrade Admin · Accepted Answer

4 x2-16 x+λ=0 f(1)>0 and f(2)<0 f(3) >0

4-16+λ >0 λ >12 f(2)=16-32+λ <0 λ <16 f(3)=36-48+λ >0 λ >12 12 < λ< 16 So λ=13,14,15 has 3 integral solutions.

Q. If $α, β$ be the roots of $4 x^{2} - 16 x + λ = 0$ , where $λ \in R$ , such that $1 < α < 2$ and $2 < β < 3$ , then the number of integral values of $λ$ is

5

6

2

3

$4 x^{2} - 16 x + λ = 0$
$f (1) > 0$ and $f (2) < 0 f (3) > 0$

$4 - 16 + λ > 0$
$λ > 12$
$f (2) = 16 - 32 + λ < 0$
$λ < 16$
$f (3) = 36 - 48 + λ > 0$
$λ > 12$
$12 < λ < 16$
So $λ = 13, 14, 15$ has 3 integral solutions.

Q. If α,β be the roots of 4x2−16x+λ=0, where λ∈R, such that 1<α<2 and 2<β<3, then the number of integral values of λ is

5

6

2

3

4x2−16x+λ=0 f(1)>0 and f(2)<0f(3)>0 4−16+λ>0 λ>12 f(2)=16−32+λ<0 λ<16 f(3)=36−48+λ>0 λ>12 12<λ<16 So λ=13,14,15 has 3 integral solutions.

Q. If $α, β$ be the roots of $4 x^{2} - 16 x + λ = 0$ , where $λ \in R$ , such that $1 < α < 2$ and $2 < β < 3$ , then the number of integral values of $λ$ is

$4 x^{2} - 16 x + λ = 0$
$f (1) > 0$ and $f (2) < 0 f (3) > 0$

$4 - 16 + λ > 0$
$λ > 12$
$f (2) = 16 - 32 + λ < 0$
$λ < 16$
$f (3) = 36 - 48 + λ > 0$
$λ > 12$
$12 < λ < 16$
So $λ = 13, 14, 15$ has 3 integral solutions.