Question

If alpha +beta are the zeroes of the polynomial 2x^2+5x+k,find the value of k such that (alpha+beta)^2-alpha×beta=24

Answer 1

heya

here is your answer

2x²+5x+k=0
 
sum of the zeroes = α+β
                              =-b/a=-5/2
product of the zeroes=αβ
                                  =c/a=k/2

(α+β)²-αβ=24
25/4 - k/2 = 24
50-4k/8=24
50-4k=192
-4k = 192-50
-4k=142
k=--71/2