I would welcome your advice on my workings in this question with particular reference to part (ii).
Thanking you in advance.
The roots of the quadratic equation are
(i) prove that ;
;
; Hence
(ii) Find, in terms of , a quadratic equation in , whose roots are and .
Formula for quadratic equation where and are the roots of the equation :
- sum of roots + product of roots;
Where the equation's roots are and : we know from (i) above that and that ;
so - sum of roots + product of roots = 0 implies
According to the textbook the answer is
I might have erred earlier on, but from my workings shouldn't the answer be
in other words, one cannot multiply by 2 across the equation as that 2 is part of a fraction that should be squared.
Thank you for taking the time to read this post.
(sighs)
I spent about 10 minutes looking at this and after posting several versions of different things that would make the post make more sense and all I can come up with is that Plato's right. This is sheer gibberish.
@seaniboy You are going to have to repost this after a lot of editing. Start with Plato's suggestions.
-Dan
Thank you for that explanation. Following your workings, we get the equation:
1. ; however, the answer in the textbook is:
2. , which is multiplying the coefficient of each term by 2.
QUESTION: given that 2 is part of a fraction in the last term of the equation that should be squared - see 1. above, why are the coefficients not multiplied by 4 instead?
Apologies for being awkward and thank you once again for explaining so clearly.
Sean.