1
$\begingroup$

In this image you can see an Ex 3 I have formed the auxilary Eqn i, but i am not able to solve the auxilary eqn with degree 4 , and find the roots of the eqn

$\endgroup$
  • $\begingroup$ There are "obvious" roots to $m^4-m^3-9 m^2-11 m-4=0$; at least, $m=-1$ is a double root. Just continue ! $\endgroup$ – Claude Leibovici May 6 '17 at 5:02
  • 1
    $\begingroup$ @projectilemotion. I know that; I just wanted the user to finish the work ! Cheers. $\endgroup$ – Claude Leibovici May 6 '17 at 6:04
1
$\begingroup$

Notice that at one point during your calculations, you somehow 'converted' a minus sign into a plus sign. Your auxilliary equation should be: $$m^4-m^3-9m^2-11m\color{red}{-}4=0$$ Using the Rational Root Theorem, we know that $m=4$ is a solution to your auxilliary equation.

Using polynomial division, we obtain: $$\frac{m^4-m^3-9m^2-11m-4}{m-4}=m^3+3m^2+3m+1, m\neq 4$$ Notice that this may be factored to give $(m+1)^3$. Hence, $m=-1$ is a root of multiplicity $3$.

Can you continue, and find the general solution from this?

$\endgroup$
  • $\begingroup$ Thnku so much @projectilemotion's 😊 $\endgroup$ – Akshie Dhiman May 6 '17 at 8:10

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.