Question

Find the sum of reciprocals of the zeros of x2 + 6x + 2 (a) 3 (b) -3 (c) 12 (d) -12​

Answer 1

Given:

The Polynomial x² + 6x + 2

To find :

The sum of reciprocals of the zeros of x² + 6x + 2

Formula to be used:

Sum of the roots ( α + β ) =  $\frac{-b}{a}$

Product of the roots ( αβ ) =  $\frac{c}{a}$

Solution:

Step 1 of 2:

Let, α and β are the two roots of the equation.

To find the sum of reciprocals of the zeros,

Sum of reciprocals of the zeros = ( 1 / α ) + ( 1 /β)

Sum of reciprocals of the zeros =  ( α + β ) / αβ

Step 2 of 2:

To find the values of  ( α + β ) and αβ from the equation we get ,

a = 1

b = 6

c  = 2

Sum of the roots ( α + β ) =  $\frac{-6}{1}$

Product of the roots ( αβ ) =  $\frac{2}{1}$

Sum of reciprocals of the zeros =  ( α + β ) / αβ

Sum of reciprocals of the zeros = $\frac{\frac{-6}{1}}{\frac{2}{1}}$

Sum of reciprocals of the zeros = $\frac{-6}{1}$ × $\frac{1}{2}$

Sum of reciprocals of the zeros = $\frac{-6}{2}$  

Sum of reciprocals of the zeros = -3

Final answer:

The sum of reciprocals of the zeros of  x2 + 6x + 2 is -3.  

Thus, the correct option is (b) -3