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If alpha and beta are the zeros of a quadratic polynomial x^2-5x+k and alpha-beta =1 then find tha value of k

    • Posted by Saurav Kumar 5 years, 3 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Gaurav Seth 5 years, 3 months ago

    x2-5x+k

     Here, a=1, b=-5 and c=k 

    Now, α+ β = -b/a= -(-5)/1= 5 

    α*β  = c/a= k/7= k

     Now,α - β =1

     Squaring both sides, we get,

     (α - β)2=12 

    ⇒ α2 + β2 - 2αβ = 1

    ⇒ (α2 + β2 + 2αβ) - 4αβ = 1

    ⇒ (α +β)2 -4αβ =1

    ⇒ (5)2-4k=1

    ⇒ -4k= 7-25

     ⇒ -4k= -24 

    ⇒ k=6 So the value of k is 6. 

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