Question

If alpha and beta are the zeroes of the quadratic polynomial p(x)=4x^2-5x-1 find the value of alpha^2 multiply beta plus alpha multiply beta ^2

Answer 1

Hi there !

To find :- α²β +aβ²


α²β +aβ² = αβ [α +β ]

4x²-5x-1 can be written as :-
ax² + bx+ c
here ,
a = 4 , b = -5 , c = -1
alpha and beta are the zeroes of the quadratic polynomial

Product of the zeroes [ αβ] = c/a = -1/4

Sum of the zeroes [α +β ]= - b/a - [ -5] /4 = 5/4



α²β +aβ² = αβ [α +β ]
= - 1/4 x 5/4
= -5/16

α²β +aβ² = -5/16