alpha and beta quadratic equation roots

Hi I'm trying to solve the roots of x^2+5x+3=0 whose roots are 2α+ß and α+2ß.

I've already solved the sum which is -15 but I'm having trouble with the product.

I multiplied the roots to give me 2α^2 +5αß + 2ß^2 but now I don't know what to do for the α^2 and ß^2. how do I get the values for these?

btw I know that αß=3 and α+ß= -5

thanks

Are you trying to find the new equation


You need the standard result for (a+b)^2

yes I am and so should I rearrange 2α^2 + 5αß +2ß^2 to 5αß + (α+ß)^2?

thanks!

No

They are not the same

You should know that (a+b)^2 = a^2+b^2+2ab

so does that mean I should substitute (α+β)^2 - 2αβ into the equation? I'm so confused!!