Question

Given the zeroes of cubic polynomial píx): px^3 +3qx^2+3rx+s, are in the form of a-b, a, a+b find
and prove the condition
​

Answer 1

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Step-by-step explanX²+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}-8ation: