Question

Find the quadratic polynomial whose zeroes are 3+โ5 /2and 3-โ5/2

Answer 1

Heya !!!



Let Alpha = 3 + 15/2 and Beta = 3-15/2



Sum of zeroes = Alpha + Beta








=> ( 3 + 15/2 + 3 - 15/2 )





=> ( 3 + 15 + 3 - 15)/2





=> 6/2 = 3





And,




Product of zeroes = (Alpha × Beta )






=> ( 3 + 15/2) × (3-15/2)





=> (3/2)² - (15/2)²




=> 9/4 - 225/4






=> 9-225/4




=> -216/4





=> -54





Therefore,


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






=> X² - (3)X + (-54)





=> X² -3X - 54



★ HOPE IT WILL HELP YOU ★