Answer:
-4/5
Step-by-step explanation:
Let α and β be the roots of the quadratic equation
ax²+bx+c = 0
Sum of roots α + β = -b/a
Product of roots αβ = c/a
Given the equation 16x²+4x+5 = 0
a = 16, b = 4, c = 5
Sum of roots α + β = -4/16 = -1/4
Product of roots αβ = 5/16
To calculate 1/α + 1/β, we will need to find the LCM first'
1/α + 1/β
= (β+α)/αβ
= sum of roots/product of roots
= (-1/4)/(5/16)
= -1/4×16/5
= -4/5
