Question

if alpha and beta are zeroes of polynomial p(x)=x^-(k+6)x+2(2k-1)then find the value of k if aipha +beta=alpha×beta/2

Answer 1

hey

let alpha be a and beta be b (for my convenience)

2(a+b) = ab
2(k-6) = 4k - 2
2k - 6 = 4k - 2
4k - 2k = -6 + 2
2k = -4
k = -4/2
k = -2

Answer 2

Answer:

k=7

Step-by-step explanation:

α+β=1/2×α×β

α+β= -b/a = -[ - (k+6)]

α×β= c/a = 2(2k-1) = 4k-2

Therefore,

k+6 = 1/2 ×( 4k-2)

2(k+6) = 4k-2

2k+12 = 4k-2

-4k+2k = -2-12

k = -14/-2

k=7