If α and β are the roots of the equation x²+5x+6=0, then the value of  αβ - ($$\frac1α$$ + $$\frac1β$$​) is:

Correct option is C

Given:

The quadratic equation is x²+5x+6=0
Roots are α and β
We need to find the value of αβ - ($$\frac1\alpha$$​+$$\frac1β$$​)

Formula Used:

For equation $$ax^2 +bx+c = 0$$ 

Sum of roots = $$\frac{-b}{a}$$ 

Product of roots = $$\frac{c}{a}$$​​

Solution: 

x²+5x+6=0 

Now, 

α+β = -$$\frac{b}a$$ = -$$\frac51$$ = -5

αβ = $$\frac{c}a$$ = $$\frac61$$ = 6 

So, 

αβ − ($$\frac1α$$​+$$\frac1β$$) 

= αβ − $$\frac{α+β}{αβ}$$ 

= 6 - $$\frac{-5}6$$ 

= 6 + $$\frac56$$​ 

= $$\frac{36+5}6$$ 

= $$\frac{41}6$$​​