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 ;
(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.