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Question :a and ß are the roots of the quadratic polynomial p(x)=x^2-(k-6)x+2(2k-1).Find the value of k,if a+ß=1/2aß.♻️Moderator™♻️Content Quality Answer Needed ✔️​

Answer»

<P>Correct Question:

α and β are the zeroes of the quadratic polynomial p(x) = x² - ( K - 6 )x + 2(  2k - 1 ). Find the value of k, if α + β = ( 1/2 ) × αβ

Answer:

- 5

Step-by-step explanation:

Given :

α and β are the zeroes of the quadratic polynomial p(x) = x² - ( k - 6 )x + 2(  2k - 1 ).

COMPARING x² - ( k - 6 )x + 2(  2k - 1 ) with ax² + bx + c we get,

  • a = 1
  • b = - ( k - 6 )
  • c = 2( 2k - 1 )

Sum of zeroes = α + β = - b/a = - { - ( k - 6 ) } / 1 = k - 6

Product of zeroes = αβ = c/a = { 2( 2k - 1 ) } / 1 = 2( 2k - 1 )

Given :

⇒ α + β = ( 1/2 ) × αβ

⇒ k - 6 = ( 1/2 ) × { 2( 2k - 1 ) }

⇒ k - 6 = 2k - 1

⇒ - 6 + 1 = 2k - k

⇒ - 5 = k

⇒ k = - 5

THEREFORE the value of k is - 5.


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