Question

If a and b are the zeroes of the polynomial f(x)=x^2+px+2 form a polynomial whose zeroes are (a+b)^2 & (a - b)^2

Answer 1

x²+px+2
zeroes are a and b
sum of zeroes are= -b/a
= a+b=-b/a
= a+b= -p
product of zeroes= c/a
= ab= 2
let the sum of new zeroes be S and product be P
S= (a+b)²+(a-b)²
S= p² + a²+b²-2ab
= p²+ (a+b)² - 4ab
= p² + p² - 4×2
= 2p²-8
P= (a+b)²(a-b)²
= p²× p² - 8
= p^{4} - 8
polynomial
k(x²- Sx +P)
= k(x²-(2p²-8)x+ p^{4}-8