Question

If alpha and beta are the zeroes of x2 -3x +1 then find a polynomial whose zeroes are alpha/beta , beta / alpha

Answer 1

Heya !!!

P(X) = X²-3X+1

Here,

A = 1 , B = -3 and C = 1

Sum of zeroes = -B/A

Alpha + Beta = 3/1

And,

Product of zeroes = C/A

Alpha × Beta = 1/1

Sum of the zeroes of the Quadratic polynomial whose zeroes are Alpha/Beta , Beta/Alpha

Sum of zeroes = (Alpha/Beta + Beta/Alpha)

=> ( Alpha)² + (Beta)² / Alpha × Beta

=> ( Alpha + Beta)² - 2 Alpha × Beta / Alpha × Beta

=> (3)² - 2 × 1 / 1

=> 9 - 2

=> 7

And,

Product of zeroes = ( Alpha / Beta × Beta / Alpha)

=> ( Alpha × Beta ) / ( Alpha × Beta )

=> 1

Therefore,

Required Quadratic polynomial = X²-(Sum of zeroes)X + Product of zeroes

=> X² -7X + 1

HOPE IT WILL HELP YOU....... ;-)