Question

If alpha and beta are the zeros of the quadratic equations f (x)=x2-5x+4 then evaluate 1/alpha+1/beta-2alpha beta

Answer 1

let alpha as a

and beta as b

for convenience

now sum of roots is -b/a

a+b=5...................(1)

product of roots is c/a

ab=4

now (a-b)*2=(a+b)*2-4ab

=(-5)*2-4(4)

=25-16

=9

now we got (a-b)*2=9

(a-b)=√9

a-b=3................(2)

now add 1&2

a+b+a-b=5+3

2a=8

a=4

a+b=5

b=1

so now 1/a+1/b-2ab

1/4+1/1-2(4)1)

1/4+1-8

1/4-7

=-27/7

1/alpha+1/beta-2alpha beta=-27/7