Question

If one root of the quadratic equation 3x² – 10x + k = 0 is reciprocal of the other, find the value of k.

Answer 1

Let α and β be the roots of the equation 3x² – 10x + k = 0

∴ `α = 1/β`   ...(Given)  

⇒ αβ = 1 

⇒ `k/3 = 1`   ...`("Product of the roots" = c/a)`

⇒ k = 3  

Hence, the value of k is 3.