The Harmonic Mean (H.M.) of the roots of the equation (5 + )x² - (4 + )x + (8 + ) = 0 is -

Formula Used:

If there is a quadratic equation ax² + bx + c = 0

Then,

Sum of roots (α + β) = −b/a and,

Product of roots (αβ) = c/a

If quadratic equation that will have two roots, then the harmonic mean (HM) of two numbers α and β is given by,

HM = 

Application:

We have quadratic equation,

(5 + )x2 - (4 + )x + (8 + ) = 0

Hence,

a = (5 + )

b = - (4 + )

c =  (8 + )

Using above formula,

HM =  .... (1)

We know that,

(αβ) = c/a = 

(α + β) = −b/a = 

Putting the values of sum and product in equation (1),