If α+(1/α), β+(1/β) are zeros of f ( x )= x 2-5 x - a, where α, β ∈(0, ∞) for all x ∈ R, then the complete set of values of a is

Question

If α+(1/α), β+(1/β) are zeros of f ( x )= x 2-5 x - a, where α, β ∈(0, ∞) for all x ∈ R, then the complete set of values of a is (A) [-6, (25/4)] (B) [(-25/4), 6] (C) [(-25/4),-6] (D) ((-25/4),-6)

Tardigrade Admin · Accepted Answer

Let f ( x )= x 2-5 x - a ∴ We must have D ≥ 0 ⇒ a ≥ (-25/4) .....(1) f (2) ≥ 0 ⇒ a ≤-6 .....(2) text and (- B /2 A ) ≥ 2 ⇒ (5/2) ≥ 2 .....(3) must be satisfied simultaneously ∴(1) ∩(2) ∩(3) ⇒ α ∈(-25/4),-6

Q. If $α + \frac{1}{α}, β + \frac{1}{β}$ are zeros of $f (x) = x^{2} - 5 x - a$ , where $α, β \in (0, \infty)$ for all $x \in R$ , then the complete set of values of a is

$[- 6, \frac{25}{4}]$

$[\frac{- 25}{4}, 6]$

$[\frac{- 25}{4}, - 6]$

$(\frac{- 25}{4}, - 6)$

Q. If α+α1​,β+β1​ are zeros of f(x)=x2−5x−a, where α,β∈(0,∞) for all x∈R, then the complete set of values of a is

[−6,425​]

[4−25​,6]

[4−25​,−6]

(4−25​,−6)

Let f(x)=x2−5x−a ∴ We must have D≥0⇒a≥4−25​ .....(1) f(2)≥0⇒a≤−6 .....(2) and 2A−B​≥2⇒25​≥2<br/> .....(3) must be satisfied simultaneously ∴(1)∩(2)∩(3)⇒α∈4−25​,−6

Q. If $α + \frac{1}{α}, β + \frac{1}{β}$ are zeros of $f (x) = x^{2} - 5 x - a$ , where $α, β \in (0, \infty)$ for all $x \in R$ , then the complete set of values of a is

$[- 6, \frac{25}{4}]$

$[\frac{- 25}{4}, 6]$

$[\frac{- 25}{4}, - 6]$

$(\frac{- 25}{4}, - 6)$