Question

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

Answer 1

Let one root be α and the other root be 1/α.
The given equation is 3x² – 10x + k = 0.
Product of roots = k/3
⇒α×1/α=k/3

⇒1=k/3

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