Gate Exam Numerical Ability Quadratic Equations

The diff eqn with
D^2 + 2aD+1 = 0
is having equal roots then
a=?

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Gate Other Question

If A is sym matrix with all elements as real and trace(A)=14
max value of det(A)=?
Analytical fun with real part being e^(-y) cos(x)
imginary part is?