Question

19) If a+b, a-b are the zeroes of the
polynomial x^2 +2x + 1 then the
values of a = .................
„b =.....................
(1 Point)

Answer 1

Answer:

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Answer 2

Answer:

We are given that a polynomial

x^2+x+1x

2

+x+1

Two zeroes of polynomial are \alpha,\betaα,β .

We have to find the value of

\frac{1}{\alpha}+\frac{1}{\beta}

α

1

+

β

1

\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\beta+\alpha}{\alpha\beta}

α

1

+

β

1

=

αβ

β+α

General quadratic polynomial

x^2-(\alpha+\beta)x+\alpha\cdot \betax

2

−(α+β)x+α⋅β

Compare with given equation

\alpha+\beta=-1α+β=−1

\alpha\cdot \beta=1α⋅β=1

Substitute the values then we get

\frac{1}{\alpha}+\frac{1}{\beta}=\frac{-1}{1}=-1

α

1

+

β

1

=

1

−1

=−1

Hence, \frac{1}{\alpha}+\frac{1}{\beta}==-1

α

1

+

β

1

==−1

Step-by-step explanation:

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