Question

if alpha and beta are zeros of f(x)=4x²-5x-1 then evaluate(1)=alpha²+beta². (2) alpha³+beta³. (3). alpha⁴+beta⁴ (4) alpha²- beta²​

Answer 1

for the zeroes

a=4

b=-5

c=-1

we know that

alpha +beta= -b/a

=-(-5) /4

=5/4

and, alpha. beta=c/a

=-1/4

for(1) alpha²+beta²=(alpha+beta) ² _ alpha. beta

= (5/4) ² _ 2(-1/4)

= 25/16 - 1/2

=25 -8/16

=17/16