Question

if alpha and beta are the zeroes of the polynomial 2x²-5x+k such that alpha-beta=1/6 find value of k​

Answer 1

k= alpha-beta=1/6

alpha +beta= -b/a

so alpha + beta is 5/2

now add both the equation

we get alpha= 4/3

and beta =7/6

now alpha×beta = -c/a

so it will be -(k)/2

now multiply the alpha and beta we get

14/9

now equate 14/9=-k/2

we get k=-28/9