Question

x2-kx+6x+4k-2 value of k

Answer 1

Step-by-step explanation:

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

Hence, the value of k is 7

HOPE THIS WILL HELP YOU...

Answer 2

Answer:

k = 7

Step-by-step explanation:

Equation is x^2 - kx + 6x + 4k - 2

We can write the equation as,

=> x^2 - (k + 6)x + 2(2k - 1)

Let us compare with ax^2 + bx + c = 0

We will get a = 1, b = -(k + 6), c = 2(2k - 1)

Let the zeroes be α,β.

Sum = (k + 6)

Product = 4k - 2

We have,

α+β = 1/2αβ

=> (k+6)=1/2(4k-2)

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

=> 2k + 12 = 4k - 2

=> k = 7

Hence, the value of k = 7.

#Hope my answer will help you