Help with question 11? (1 Viewer)

[Bob_man]

I've found the values for m (-12 and -20), but im not sure how to find α and β. The answers were apparently 1±√5 and -3±√5.

 

[jimmysmith560]

My knowledge of polynomials is rather rusty, but given the fact that you found the values of m, you can substitute each value into the original equation and find the roots:

Starting with :




One of the roots will be , but according to the answer, it seems that we should disregard this, leaving us with:



i.e. , matching the answer provided.

Moving on to :




One of the roots will be , but according to the answer, it seems that we should disregard this, leaving us with:



i.e. , matching the answer provided.

There appears to be a different approach that would require the use of simultaneous equations, although I am not exactly sure as to how that would be performed.

I hope this helps!

 

[5uckerberg]

I've found the values for m (-12 and -20), but im not sure how to find α and β. The answers were apparently 1±√5 and -3±√5. View attachment 34884

Since you have shown that m=-12 and -20 then the style of attack would be to experiment with the fact that .
First and foremost depending on the sum and product of roots we can see clearly that if then m=-20 and if then m=-12. At this point, we start experimenting and therefore m=-20 one of your factors will look like this and for m=-12 then one of your factors will look like this . Use any method possible (Quadratic, complete the square or Po-Shen Loh method or etc.) find the roots

 

[Bob_man]

Thanks guys!