Q1 of 180 Page 5

If the sum of the

Let the roots of the given quadratic equation 3x2-(3k-2)x-(k-6)=0 be α and β.


Now,


sum of roots = α+β = (3k-2)/3 and,


product of roots = αβ = -(k-6)/3


[∵ If α and β are the roots of quadratic equation ax2+bx+c=0 then α+β = -b/a and αβ = c/a]


According to question-


sum of roots = product of roots


∴ α+β = αβ


⇒ (3k-2)/3 = -(k-6)/3


⇒ 3k-2 = -k+6


⇒ 4k = 8


∴ k = 2


Hence, the value of k is 2.


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