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.