Question

x square-(k+6)x+2(2k-1). find the value of k if alpha+ beta =1/2alpha *beta​

Answer 1

Step-by-step explanation:

given p(x) = x² - (k+6)x + 2(2k-1)

α+β = 1/2*αβ

in the given polynomial p(x),

a = 1, b = -(k+6) and c = 2(2k-1)

α+β = -b/a and αβ = c/a

it is given that α+β = 1/2*αβ

=> 2(α+β) = αβ

=> 2(-b/a) = c/a

=> -2b = c

=> -2[-(k+6) = 2(2k-1)

=> 2k+12 = 4k-2

=> 12+2 = 4k - 2k

=> 14 = 2k

=> k = 7