Question

find value of k.....​

Answer 1

Answer:

k=7

Step-by-step explanation:

x²-(k+6)x+2(2k-1)

α+β=k+6, αβ=2(2k-1)=4k-2

α+β=½αβ

k+6=½(4k-2)

k+6=½×2(2k-1)

k+6=2k-1

k-2k=(-1)-6

(-k)=(-7)

k=7

Answer 2

Solution :

• x² - ( k +6) x + 2 (2k -1)

Here ,

• a = 1 , b = - (k +6) and c = 4k -2

$\implies \: \alpha + \beta = \frac{1}{2} \alpha \beta \\ \\ \implies \: \frac{ - b}{a} = \frac{1}{2} \frac{c}{a} \\ \\ \implies \: \frac{ - ( - (k + 6))}{1} = \frac{1}{2} \frac{4k - 2}{1} \\ \\ \implies \: k + 6 = 2k - 1 \\ \\ \implies \: 2k - k = 6 + 1 \\ \\ \implies \: k = 7$

Hence , the value of k is 7.