Question

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

Answer 1

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.