Question

Sum of zeroes and reciprocal of its zeroes of a polynomial are 10 and 12.5 respectively. What is the product of zeroes of that polynomial?
1. 0.5
2. 1
3. 0.8
4. 1.5

Answer 1

Correct Answer - Option 3 : 0.8

Given:

α + β = 10   

1/α + 1/β = 12.5 

Concept:

If α and β are the zeroes of a polynomial then,

Sum of zeroes = α + β

Product of zeroes = αβ

Calculation:

α + β = 10                                          …………………(1)

1/α + 1/β = 12.5                           

⇒ (α + β)/αβ = 12.5                           ……………………..(2)

From equation (1) and (2)

⇒10/ αβ  = 12.5 = 25/2

⇒ αβ = 20/25

⇒ αβ = 4/5

∴ The product of zeroes of  polynomial is 0.8

The correct option is 3 i.e. 0.8