Question

If alpha and beta are the zeroes of the quadratic polynomial f(x) = x2 - px + q, prove that alpha2/beta2 + beta2/alpha2 = p4/q2 - 4p2/q + 2

Answer 1

hey friend !!!!


Now,

let me denote 'alpha' by 'a' and 'beta' by 'b'

so, a + b = p , ab = q

now

a2/b2 + b2/a2 = a4+b4/(ab)2

use, a4 + b4 = (a2 + b2)2 - 2a2b2

  = [(a + b)2 - 2ab]2 - 2(ab)2

Now, a + b = p and ab = q


(p2-2q)2-2q2 = p4+4q2-4qp2-2q2

put these values the above expression and divide it by (ab)2

Now

a2/b2 + b2/a2 = (p4+4q2-4qp2-2q2)/(q)2

= p4/q2 + 4p2/q + 2______proved

hope it will help you


if any doubt plz comment in comment box

Answer 2

Answer:

I've attached the answer I hope it helps you....

Step-by-step explanation: