if the zeroes of the polynomial x2-5/2x+k are reciprocal of each other, find the value of k ?

Answer 1

In guadratic equation a x² + b x + c = 0

Product of roots = c / a

If your expression mean:

x² - ( 5 / 2 ) x + k = 0 then

In this equqation:

a = 1 , b = - 5 / 2 , c = k

In quadratic eguation product of roots = c / a = k / 1 = k

Given that the roots are reciprocals of each other.

If one root is p, the other would be 1 / p their product will be 1.

So:

Product of roots:

p ∙ 1 / p = 1

Product of roots also:

c / a = k

So k = 1

By the way the soutions of:

x² - ( 5 / 2 ) x + 1 = 0

are

x = 2 and x = 1 / 2