Question

if alpha and beta are the zeroes of the polynomial f(x)=x^2+x-2,find the value of 1/alpha+1/beta​

Answer 1

If α,β are the zeros of the polynomials f(x)=x

2

+x+1 then

α

1

+

β

1

=________.

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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.

Answer 2

Step-by-step explanation:

x²+x-2

its zeroes are alpha and beta

alpha + beta = -1/1

alpha ×beta = -2/1

to find- 1/ alpha +1/beta

1(beta) + 1(alpha)/alpha × beta

alpha + beta / alpha × beta

-1/-2

= 1/2