find the value of k, so that the difference of roots of x²-5x+3(k-1) =0 is 11
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Let α and β are the roots of the quadratic equation.
Given quadratic equation is x² - 5x + 3(k -1) = 0.
α - β= 11 …………(1)
On comparing with ax² + bx + c
a= 1 , b= -5, c= 3(k-1)
Sum of zeroes (α+β) = -b/a
(α+β) = -b/a
(α+β) = -(-5)/1= 5
(α+β) = 5……………..(2)
On Adding Equations 1 and 2,
α - β= 11
α + β = 5
---------------
2α = 16
α = 16/2
α = 8
On putting α = 8 in eq 1,
α - β= 11
8 - β = 11
8-11 = β
β = -3
Product of zeroes(α.β)= c/a
8 × -3 = 3(k-1)/1 [α = 8 , β = -3]
-24 = 3(k-1)
-24 = 3k -3
-24 +3 = 3k
-21 = 3k
k = -21/3
k = -7
Hence, the value of k = -7.
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