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a and b are the zeroes of the polynomial x2- (k+6)x+2(2k-1) find the value of k if a +b=1/2ab

it's not a and b it's alpha and beta

answer it

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hey dear friend!!!!

Let α and β are zeroes of the polynomial = x² - (k + 6)x + 2(2k –1).

On comparing with ax²+bx+c=0

a= 1,

b= -( k+6) ,

c = 2(2k –1)

Sum of zeroes (α+β)= -b/a = -(-(k+6))/1

α+β= (k+6)…………....(1)

Product of zeros(α.β)= c/a = 2(2k –1)/1

α.β= c/a = 4k -2…………(2)

Given: (α+β) = ½(αβ )

=> (k+6) = ½( 4k -2)

[From eq 1 & 2]

=> 2 (k +6 )= 4k -2

=> 2k +12 = 4k -2

=> 2k -4k = -2 -12

=> -2k = -14

=> k = 14/2

=>k = 7______answer

Hence, the value of "k is 7"

HOPE THIS WILL HELP YOU...

Let α and β are zeroes of the polynomial = x² - (k + 6)x + 2(2k –1).

On comparing with ax²+bx+c=0

a= 1,

b= -( k+6) ,

c = 2(2k –1)

Sum of zeroes (α+β)= -b/a = -(-(k+6))/1

α+β= (k+6)…………....(1)

Product of zeros(α.β)= c/a = 2(2k –1)/1

α.β= c/a = 4k -2…………(2)

Given: (α+β) = ½(αβ )

=> (k+6) = ½( 4k -2)

[From eq 1 & 2]

=> 2 (k +6 )= 4k -2

=> 2k +12 = 4k -2

=> 2k -4k = -2 -12

=> -2k = -14

=> k = 14/2

=>k = 7______answer

Hence, the value of "k is 7"

HOPE THIS WILL HELP YOU...

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