Inverse Laplace Transform:

\[ \frac{2s^2 - 9s - 35}{s^2 + 4s + 2} \]

Choose the correct expression:

a) $\frac{2s^2 - 9s - 35}{s^2 + 4s + 2}$

b) $\frac{s^2 + 4s + 2}{2s^2 - 9s - 35}$

c) $\frac{s^2 - 4s - 2}{2s^2 + 9s + 35}$

d) $\frac{2s^2 + 9s + 35}{s^2 - 4s - 2}$

Question

29-08-2025
Mathematics

High School

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Inverse Laplace Transform:

\[ \frac{2s^2 - 9s - 35}{s^2 + 4s + 2} \]

Choose the correct expression:

a) $\frac{2s^2 - 9s - 35}{s^2 + 4s + 2}$

b) $\frac{s^2 + 4s + 2}{2s^2 - 9s - 35}$

c) $\frac{s^2 - 4s - 2}{2s^2 + 9s + 35}$

d) $\frac{2s^2 + 9s + 35}{s^2 - 4s - 2}$

Answer :

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Final Answer:

The correct option for the inverse Laplace transform of [tex]$ \frac{2s^2 - 9s - 35}{s^2 + 4s + 2} $ is b) $ \s² + 4s + 2\2s² - 9s - 35 $[/tex].

Explanation:

Inverse Laplace transforms involve finding the original function from its Laplace transform. In this case, the expression [tex]$ \frac{2s^2 - 9s - 35}{s^2 + 4s + 2} $[/tex] can be factored into [tex]$ \frac{(2s + 5)(s - 7)}{(s + 2)^2} $[/tex]. The numerator's roots are 5 and -7, while the denominator has a repeated root of -2. Therefore, the inverse Laplace transform is a combination of terms like [tex]$ e^{-2t} $ and $ e^{-7t} $[/tex] along with polynomial terms.

The correct option, b), represents the correct order of terms in the inverse Laplace transform. The terms [tex]$ \s² + 4s + 2 $[/tex] indicate the polynomial part of the inverse Laplace transform, and the arrangement corresponds to the roots of the expression. This ensures an accurate representation of the original function when taking the inverse Laplace transform.

In summary, option b) [tex]$ \s² + 4s + 2\2s² - 9s - 35 $[/tex] is the correct choice for the inverse Laplace transform of[tex]$ \frac{2s^2 - 9s - 35}{s^2 + 4s + 2} $[/tex].

Inverse Laplace Transform:\[ \frac{2s^2 - 9s - 35}{s^2 + 4s + 2} \]Choose the correct expression:a) \(\frac{2s^2 - 9s - 35}{s^2 + 4s + 2}\)b) \(\frac{s^2 + 4s + 2}{2s^2 - 9s - 35}\)c) \(\frac{s^2 - 4s - 2}{2s^2 + 9s + 35}\)d) \(\frac{2s^2 + 9s + 35}{s^2 - 4s - 2}\)

Answer :

Other Questions

Inverse Laplace Transform:

\[ \frac{2s^2 - 9s - 35}{s^2 + 4s + 2} \]

Choose the correct expression:

a) \(\frac{2s^2 - 9s - 35}{s^2 + 4s + 2}\)

b) \(\frac{s^2 + 4s + 2}{2s^2 - 9s - 35}\)

c) \(\frac{s^2 - 4s - 2}{2s^2 + 9s + 35}\)

d) \(\frac{2s^2 + 9s + 35}{s^2 - 4s - 2}\)