The value of $a_{0}$ which will ensure that the polynomial $s^{3} + 3 s^{2} + 2 s + a_{0}$ has roots on the left half of the s-plane is

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Solution

The correct option is D 5
Characteristic equation
$s^{3} + 3 s^{2} + 2 s + a_{0}$

By RH criteria

$∴$ For roots Lie on LHP
$a_{0} > 0$
$\frac{6 - a_{0}}{3} > 0$
The $a_{0}$ value should be
$0 < a_{0} < 6$
$∴ a_{0} = 5$

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The value of a0 which will ensure that the polynomial s3+3s2+2s+a0 has roots on the left half of the s-plane is

The correct option is D 5Characteristic equation s3+3s2+2s+a0 By RH criteria ∴ For roots Lie on LHP a0>0 6−a03>0 The a0 value should be 0<a0<6 ∴a0=5

The value of $a_{0}$ which will ensure that the polynomial $s^{3} + 3 s^{2} + 2 s + a_{0}$ has roots on the left half of the s-plane is

The correct option is D 5
Characteristic equation
$s^{3} + 3 s^{2} + 2 s + a_{0}$

By RH criteria

$∴$ For roots Lie on LHP
$a_{0} > 0$
$\frac{6 - a_{0}}{3} > 0$
The $a_{0}$ value should be
$0 < a_{0} < 6$
$∴ a_{0} = 5$