For what value of K roots of the equation 2x2-5x+k=0 are reciprocal to each other

Question

For what value of K roots of the equation 2x²-5x+k=0 are reciprocal to each other

(a) 2

(b) 1/2

(c) 5/2

(d) -1/2

Answer 1

Correct option (a) 2

Solution:

We have, 

2x²-5x+k=0

Product of zeroes = c/a

Let the roots be α, 1/​α

So,

α×1/α    ​  = c/a​

α×1/α ​= k/2

1 = k/2

k = 2

Then,

We get k = 2