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# Find the value of k for which the roots of the equation 3x2 -10x +k = 0 are reciprocal of each other. - Mathematics

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Sum

Find the value of k for which the roots of the equation 3x2 -10x +k = 0 are reciprocal of each other.

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#### Solution

3x2 - 10x + k = 0

∵ Roots of the given equation are reciprocal of each other.

Let the roots be α and 1/α

For a Quadratic Equation ax2 + bx + c = 0.

Sum of Roots is given by ("- b")/"a"

⟹ α + 1/α ​= (+ 10​)/3

("- b")/"a" = (10​)/3

From (1) ⟹ a = k = 3.
Concept: Nature of Roots of a Quadratic Equation
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