Question

If alfa and bitta are zeroes of the polynomial x^2+2x+1 then 1/alfa + 1/ bitta is :
a) -2
b) 2
c) 0
d) 1​

Answer 1

• Option a) -2 is the correct answer

Step-by-step explanation:

Given:

• Polynomial P(x) = x² + 2x + 1
• α and β are two zeroes of the polynomial P(x)

To find:

The value of (1/α) + (1/β)

• From the polynomial P(x)

We get, a = 1, b = 2, and c = 1

Now,

(1/α) + (1/β)

= (β + α)/αβ

[∵ by taking LCM = αβ]

Here,

(β + α) = Sum of the zeroes

And αβ = product of zeroes

So,

Sum of zeroes = ( - coefficient of x)/(coefficient of x²)  = (-b)/a = -2/1 = (-2)

And

Product of zeroes = (constant term)/(coefficient of x²) = c/a = 1/1 = 1

Now,

Putting the values in = (β + α)/αβ

= (-2)/1 = -2