Question

If alpha and beta are two zeroes of quadratic polynomial x square-(k-6)×2(2k-1). Find the value of k if alpha+beta=1 upon 2 alpha×beta

Answer 1

Step-by-step explanation:

x²- x(k-6) +2(k-1)

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

alpha +beta = -b/a = -k+6

alpha × beta = c/a = 2k-2

alpha + beta = 1/alpha× beta

implies , -k+6 = 1 / 4k- 4

= -4k² +4k +24k -24 = 1

= 4k ( 1-k) + -24 (1-k) = 1

= (4k-24 ) (1-k) = 1

= 4k -24 =1 1-k=1

= 4k = 25 k= 0 ✓

implies, k= 25/4 ✓

therefore k= 25/4 or 0

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