Question

If α and β are zeroes of x² –(k + 6)x + 2(2k –1). find the value of k if 1/α + 1/β =1/2

Answer 1

Answer:

• The required value of k is 7.

Step-by-step explanation:

We have been given that α and β are zeroes of x² –(k + 6)x + 2(2k –1). We have to find the find value of k if 1/α + 1/β =1/2.

Sum of Zeros:

• Sum of Zeros = -b/a
• Sum of Zeros( α + β)= k + 6

Product of Zeros:

• Product of Zeros = c/a
• Product of Zeros(α + β) = 4k - 2

Value of 1/α + 1/β =1/2:

1/α + 1/β =1/2

α + β/αβ = ½

α + β = ½ αβ

K + 6 = ½ * 4k - 2

2(k + 6) = 4k - 2

2k + 12 = 4k - 2

2k - 4k = -2 - 12

- 2k = - 14

2k = 14

K = 14/2

K = 7

• Therefore, the required value of k is 7.

Answer 2

Answer:

: Solution :

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Thanks .