Let A be the set of values of k for which 2 lies between the roots of the quadratic equation x2+(k + 2)x-(k + 3)=0, then A is given by

Question

Let A be the set of values of k for which 2 lies between the roots of the quadratic equation x2+(k + 2)x-(k + 3)=0, then A is given by (A) (- ∈ fty , - 5) (B) (5 , ∈ fty) (C) (-∞,-5] (D) [5, ∞)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-dbuvsq8f10j1.png" /> Opening upward parabola as the coefficient of x2 is +ve 2 lies between the roots ⇒ f(2) < 0 f(2)=4+2(k + 2)-(k + 3) < 0 4+2k+4-k-3 < 0 k+5 < 0⇒ k < -5

Q. Let $A$ be the set of values of $k$ for which $2$ lies between the roots of the quadratic equation $x^{2} + (k + 2) x - (k + 3) = 0,$ then $A$ is given by

$(- \in f t y, - 5)$

$(5, \in f t y)$

$(- \infty, - 5]$

$[5, \infty)$

Opening upward parabola as the coefficient of $x^{2}$ is $+ v e$
$2$ lies between the roots $\Rightarrow f (2) < 0$
$f (2) = 4 + 2 (k + 2) - (k + 3) < 0$
$4 + 2 k + 4 - k - 3 < 0$
$k + 5 < 0 \Rightarrow k < - 5$

Q. Let A be the set of values of k for which 2 lies between the roots of the quadratic equation x2+(k+2)x−(k+3)=0, then A is given by

(−∈fty,−5)

(5,∈fty)

(−∞,−5]

[5,∞)