If x^2-5x-14>0⇒x lie outside [α, β], then (α)/(β)=

Correct answer: (A) (-2)/7. x^2-5x-14>0 ⇒x+2x-7>0 ⇒x∈-∞,-2∪7,∞ As per question, the interval for which x lies outside is α,β ⇒α=-2, β=7 So, (α)/(β)=(-2)/7

Q50 / 160 · TS EAMCET 2021 (05 Aug Shift 1) · Mathematics

If $x^{2} - 5 x - 14 > 0 \Rightarrow x$ lie outside $[α, β],$ then $\frac{α}{β} =$

Correct answer
A
$\frac{- 2}{7}$
B
$\frac{- 7}{2}$
C
$\frac{2}{7}$
D
$\frac{7}{2}$

Solution

$x^{2} - 5 x - 14 > 0$

$\Rightarrow (x + 2) (x - 7) > 0$

$\Rightarrow x \in (- \infty, - 2) \cup (7, \infty)$

As per question, the interval for which $x$ lies outside is $[α, β]$

$\Rightarrow α = - 2$ , $β = 7$

So, $\frac{α}{β} = \frac{- 2}{7}$

Hence, the correct answer is option: 'A'.

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If x2-5x-14>0⇒x lie outside [α, β], then αβ=

Solution

Relevant Questions

If $x^{2} - 5 x - 14 > 0 \Rightarrow x$ lie outside $[α, β],$ then $\frac{α}{β} =$