Correct Answer: D
Explanation:
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.