The roots α,β of the quadratic equation x²-5x+2(k-5)=0 are such that α-β=3,find the value of k​

1 thought on “The roots α,β of the quadratic equation x²-5x+2(k-5)=0 are such that α-β=3,find the value of k​”

1. Step-by-step explanation:

   Given x

   2

   −5x+3(k−1)=0 α,β are roots is given equation.

   α−β=11 __________ (1)

   using conditions we have α+β=5

   αβ=3(k−1)

   now α−β=

   α

   2

   +β

   2

   −2αβ

   =

   (α+β)

   2

   −4αβ

   (11)

   2

   =(α+β)

   2

   −4αβ

   121−25=−12(k−1)⇒

   12

   96

   =1−k

   [k=-7]

   Hence value of k is -7.

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