How Do i get the roots of this eq?

ME433

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This is for a vibrations problem, my problem however is Algebraic.

How do I get the roots for this equation?

The roots should be

w^2 = g/l
w^2 = g/l +(2ka^2/ml^2)

For some reason have an extra term in my answer. I know my quadratic equation is correct from looking at the solution manual. My roots are not correct.
 

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At one point you have squared incorrectly.

You have \(\displaystyle \left(\frac{2ka^2}{ml^2}+ \frac{2g}{l}\right)^2\)
and then \(\displaystyle \frac{4k^2a^4}{m^2l^4}+ \frac{4g^2}{l^2}\).

That is wrong. \(\displaystyle (a+ b)^2= a^2+ 2ab+ b^2\), not \(\displaystyle a^2+ b^2\).
 
Thanks, I got the correct answer now. It seems I'm forgetting how to do Algebra as I progress into my senior level engineering classes.
 

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