Question

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

Answer 1

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f(x)=x

2

+x−2

⇒sumofroots=α+β=−1

⇒productofroots=α−β=−2....(1)

∴valueof

α

1

−

β

1

=

αβ

β−α

=

αβ

−(α−β)

....(2)

⇒α−β=

a

D

=

a

b

2

−4ac

=

1

1+4×2×1

=3

α−β=3....(3)

puttingthevalueofαβandα−βinequation(2)

⇒

α

1

−

β

1

=

−2

−(3)

=

2

3

Answer 2

Answer:

x²+x-2=0

x²+2x-x-2=0

x(x+2)-1(x+2)=0

(x+2)(x-1)=0

x=-2 or 1

alpha=-2

beta =1

1/alpha -1/beta = 1/-2 -1/1

=-3/2

ans=-3/2

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