If the difference between the roots of the equation x2 + ax + 1 = 0 is less than √5 , then the set of possible values of a is

Question

If the difference between the roots of the equation x2 + ax + 1 = 0 is less than √5 , then the set of possible values of a is (A) (−3, 3) (B) (−3, ∞) (C) (3, ∞) (D) (−∞, −3)

Tardigrade Admin · Accepted Answer

x2 + ax + 1 = 0 α + β = −a αβ =1 |α-β|=√(α+β)2-4αβ |α-β|=√a2-4 √a2-4 < √5 a2-4 < 5 a2-9 < 0 a ∈(-3, 3).

Q. If the difference between the roots of the equation $x^{2} + a x + 1 = 0$ is less than $5$ , then the set of possible values of $a$ is

$(- 3, 3)$

$(- 3, \infty)$

$(3, \infty)$

$(- \infty, - 3)$

$x^{2} + a x + 1 = 0$
$α + β = - a α β = 1$
$∣ α - β ∣ = (α + β)^{2} - 4 α β$
$∣ α - β ∣ = a^{2} - 4$
$a^{2} - 4 < 5$
$a^{2} - 4 < 5 < b r / > a^{2} - 9 < 0$
$a \in (- 3, 3) .$

Q. If the difference between the roots of the equation x2+ax+1=0 is less than 5​ , then the set of possible values of a is

(−3,3)

(−3,∞)

(3,∞)

(−∞,−3)