Question

The equation 2x^2 + x -4 =0 has roots a and beta and the equation x^2 - 2x + p =0 has roots k(a)/beta and k(beta)/a. Find the value of k and of p.

Answer 1

?

Answer 2

first find what a and beta are I think

Answer 3

2x^2 + x -4 =0 has roots a and beta

means you can factor the quadratic into 2(x-a)(x-b)=0
expanding, you get 2(x^2 - a x - b x +ab) =0 or
2x^2 - 2(a+b) x + 2ab = 0

match corresponding terms to find: -2(a+b) = 1 or (a+b)= -1/2
2ab= -4 or ab = -2

now do the same thing for the 2nd polynomial
x^2 - 2x + p =0 has roots k(a)/beta and k(beta)/a

expand
(x - k a/b)(x - k b/a)

and match corresponding terms of x^2 - 2x + p =0

you will need to use the "trick" that (a+b)^2 = a^2 + b^2 +2ab from which you get
a^2 + b^2 = (a+b)^2 - 2ab