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Question:

Find the value of k for which the roots of the equation 3x^2 - 10x + k = 0 are reciprocal of each other.

Solution:

Let the roots be α, 1/α
For a Quadratic Equation ax^2 + bx + c = 0
Sum of Roots is given by -b/a
α + 1/α = +10/3
-b/a = 10/3
From (1) α = k = 3