Question

The roots α and β of the quadratic equation x² -5x + 3 (k-1) = 0 are such that α-β =1 .
Find the value of k.

Answer 1

Answer:

α + β = 5 --- (1)

α - β = 1 --- (2)

Solving (1) and (2), we get

α = 3 and β = 2

Also αβ = 6 Or 3(k - 1) = 6

k - 1 = 2

k = 3

Answer 2

→ Hey Mate,  

→ Given Question:-

→ The roots α and β of the quadratic equation x² - 5x + 3 (k-1) = 0 are such that α - β = 1.  Find the value of k.

→ To Find:-

→ Find the value of k?

→ Solution:-

→ x² -5x + 3( k - 1) = 0

→ α = 1

→ β = -5

→ c = 3 (k - 1)

→ α - β = 1

→ α - 1 = β

→ Sum of roots = α + β = -b / α

→                        = α  + α - 1 = - ( -5) / 1

→                        = 2α - 1 = 5

→                        = 2α = 6 (∵ 2 and 6 gets cancels)

→                  so, = α = 3

→                           β = α - 1

→                              = 3 - 1

→                              = 2

→ so , β = 2

→ Product of roots = αβ = c / a

→                             = 3(2)  = 3k - 3 / 1

→                             = 6      = 3k - 3

→                             = 6 + 3 = 3k

→                             =   9     = 3k

→                             =   k = 3

→ ∴ The Value of k is 3.

→ More Information:-

→ brainly.in/question/28553023?tbs_match=4&referrer=searchResults#:~:text=The%20roots%20%CE%B1,Find%20the%20value%20k

→ brainly.in/question/37510443?tbs_match=4&referrer=searchResults#:~:text=185.1K%20people%20helped-,Solution,-Given%20%3A-

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