Question

if one zero of 2 x square - 3 x + K is reciprocal to the other then find the value of k​

Answer 1

Answer:

The value of k is 2

Step-by-step explanation:

$The\ polynomial\ is\ 2x^2-3x+k=0,\ where\ a=2,\ b= -3,\ c=k$

We know, sum of zeroes is given by $\frac{-b}{a}\\ whereas\ product\ of\ zeroes\ is\ given\ by\ \frac{c}{a}$

Now it's being given that, one zero is the reciprocal of the other.

So, the two zeroes are $\rm \alpha and \frac{1}{\alpha}$

Now, according to the question

$\rm \alpha\times \frac{1}{\alpha}=\frac{k}{2}\\ \\ \implies 1=\frac{k}{2}\\ \rm by\ cross\ multiplication\\ \therefore k=2$