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 k.

Answer 1

Answer:

Step-by-step explanation:

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 k.

→ To 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 / a

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

→                       =  2α -1     =  5

→                       =  2α  = 5 + 1

→                       = 2α   = 6

→ α = 3

→ β = 2

→  β = α - 1

→     = 3 - 1

→     = 2

→ Product of Roots ⇒

→ αβ = c / α

→ 3(2) = 3k - 3 / 1

→ 6  = 3k - 3

→ 6 + 3 = 3k

→ 3  9  = 3 k  ( ∵ here 9 and 3 gets cancel)

→ k = 3

→ so, the value of k is 3.  

→ More Explanation :-

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

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