If x1 and x2 are the roots of the equation 2 x2+6 x+a=0 satisfying the relation (x1/x2)+(x2/x1)

Question

If x1 and x2 are the roots of the equation 2 x2+6 x+a=0 satisfying the relation (x1/x2)+(x2/x1)<2 then 'a' must lie in the interval (A) (-∞, 0) (B) (-∞, 0) ∪((9/2), ∞) (C) (0, (9/2)) (D) ((9/2), ∞)

Tardigrade Admin · Accepted Answer

Note that roots are real. Hence also the condition D >0

Q. If $x_{1}$ and $x_{2}$ are the roots of the equation $2 x^{2} + 6 x + a = 0$ satisfying the relation $\frac{x _{1}}{x _{2}} + \frac{x _{2}}{x _{1}} < 2$ then 'a' must lie in the interval

$(- \infty, 0)$

$(- \infty, 0) \cup (\frac{9}{2}, \infty)$

$(0, \frac{9}{2})$

$(\frac{9}{2}, \infty)$

Note that roots are real. Hence also the condition D $> 0$

Q. If x1​ and x2​ are the roots of the equation 2x2+6x+a=0 satisfying the relation x2​x1​​+x1​x2​​<2 then 'a' must lie in the interval

(−∞,0)

(−∞,0)∪(29​,∞)

(0,29​)

(29​,∞)