Question

If α, β are the zeros of the polynomial p(x) = x2+x+1, then value of + is?

Answer 1

Step by step explanation

ANSWER

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.

Do it in the same way