Question

If a, B are the zeroes of the polynomials x^2+x+ 1 then 1/a+1/b is
​

Answer 1

Answer:

−1

Step-by-step explanation:

f(x)=x  

2

+x+1

a=1

b=1

c=1

∵α and β are the zeroes of above polynomial.

∴ Sum of roots =  

a

−b

​

 

⇒α+β=  

1

−1

​

 

⇒α+β=−1⟶(1)

Product of roots =  

a

c

​

 

⇒αβ=  

1

1

​

 

⇒αβ=1⟶(2)

∴  

α

1

​

+  

β

1

​

=  

αβ

β+α

​

 

From eq  

n

(1)&(2), we have

⇒  

α

1

​

+  

β

1

​

=  

1

−1

​

=−1

Hence, -1 is the correct answer.

Answer 2

Answer:

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Question :-

• If a, B are the zeroes of the polynomials x^2+x+ 1 then 1/a+1/b is

Solution :-

f (x) = x^2 + x + 1

Where, a = 1 , b = 1 , c =1

One zero = a

Second zero = b

Sum of zeroes ( a + b ) = - b/a = -1 / 1 = -1

Product of zeroes ( a × b ) = c/a = 1 / 1 = 1

We have to find value of , 1 / a + 1 / b

Taking LCM

= a + b / ab

Keeping the values now,

= -1 / 1

= -1

Thus, 1 / a + 1 / b = -1