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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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