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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

The given equation is `3"x"^2 - 10"x" + "k" = 0`
Roots of the given equation are reciprocal of each other.
Let α and `1/alpha` be the roots of the given equation.
Product of roots = `c/alpha`

⇒ α . `(1)/α = "k"/(3)`

⇒ `"k"/(3) = 1`

⇒ `"k" = 3`

Concept: Nature of Roots
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