The smallest integral value c of x such that (x-5/x2+5 x-14) 0, satisfies

Question

The smallest integral value c of x such that (x-5/x2+5 x-14) >0, satisfies (A) c 2+3 c -4=0 (B) c 2-7 c +6=0 (C) c 2-5 c +4=0 (D) c2+5 c-6=0

Tardigrade Admin · Accepted Answer

(x-5/x2+5 x-14)>0 ⇒ (x-5/x2+7 x-2 x-14)>0 ⇒ (x-5/(x+7)(x-2))>0 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/0fde64b72cc7d7c9324edb7a5ade3b54-.png" /> ⇒ x ∈(-7,2) ∪(5, ∞) Smallest integral value of x=0=-6 which is root of equation c 2+5 c -6=0.

Q. The smallest integral value $c$ of $x$ such that $\frac{x - 5}{x ^{2} + 5 x - 14} > 0$ , satisfies

$c^{2} + 3 c - 4 = 0$

$c^{2} - 7 c + 6 = 0$

$c^{2} - 5 c + 4 = 0$

$c^{2} + 5 c - 6 = 0$

$\frac{x - 5}{x ^{2} + 5 x - 14} > 0 \Rightarrow \frac{x - 5}{x ^{2} + 7 x - 2 x - 14} > 0 \Rightarrow \frac{x - 5}{( x + 7 ) ( x - 2 )} > 0$

$\Rightarrow x \in (- 7, 2) \cup (5, \infty)$
Smallest integral value of $x = 0 = - 6$
which is root of equation $c^{2} + 5 c - 6 = 0$ .

Q. The smallest integral value c of x such that x2+5x−14x−5​>0, satisfies

c2+3c−4=0

c2−7c+6=0

c2−5c+4=0

c2+5c−6=0