Question

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : Every solution of the differential equation $y'' + 2y' + 2y = 0$ tends to zero as $x \to \infty$.
Reason R : The real part of the roots of the polynomial $\lambda^2 + 2\lambda + 2$ are negative.
In the light of the above statements, choose the correct answer from the options given below

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true but R is NOT the correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Hint:

Stability Condition: In $y'' + a y' + b y = 0$, every solution $\to 0$ as $x \to \infty$ if and only if $a > 0$ and $b > 0$ (Routh-Hurwitz criterion for order 2). Here $a = 2 > 0$ and $b = 2 > 0$, confirming asymptotic stability!

Answer 1

The Correct Option is A