Question

if alpha and beta are zero of polynomial p (x) = 4x2 -5x -1 then find value of alpha 2beta + alphabeta2

Answer 1

Equation = 4x² - 5x - 1

=> Sum of roots = - b / a = - ( - 5 ) / 4 = 5 / 4

=> Product of roots = c / a = - 1 / 4

α²β + αβ² = ( α + β ) × αβ

=> α²β + αβ² = ( 5 / 4 ) × - 1 / 4

=> α²β + αβ² = ( - 5 / 16 )

Hope it helped !