Question

If one root of the quadratic equation 3x^2-10x+k=0 is reciprocal of the other then find the value of k

Answer 1

hope this will help you all

Answer 2

Answer:

The value of k is 3.

Step-by-step explanation:

The given quadratic equation is

$3x^2-10x+k=0$

It is given that one root of this quadratic equation is reciprocal of the other.

Let the roots be $\alpha \text{ and } \frac{1}{\alpha}$.

We know that,

$\text{Sum of roots}=\frac{-b}{a}$                    ....(1)

$\text{Product of roots}=\frac{c}{a}$               ....(2)

Using equation (2) we get

$\alpha \times \frac{1}{\alpha}=\frac{k}{3}$

$1=\frac{k}{3}$

Multiply both sides by 3.

$3=k$

Therefore the value of k is 3.