Question

X^2=x-1=0 find nature of root

Answer 1

please explain in detail

Answer 2

Step-by-step explanation:

If you have a quadratic equation of the form

a

x

2

+

b

x

+

c

=

0

The solution is

x

=

−

b

±

√

b

2

−

4

a

c

2

a

The discriminant

Δ

is

b

2

−

4

a

c

.

The discriminant "discriminates" the nature of the roots.

There are three possibilities.

If

Δ

>

0

, there are two separate real roots.

If

Δ

=

0

, there are two identical real roots.

If

Δ

<

0

, there are no real roots, but there are two complex roots.

Your equation is

x

2

+

x

+

1

=

0

Δ

=

b

2

–

4

a

c

=

1

2

−

4

×

1

×

1

=

1

–

4

=

−

3

This tells you that there are no real roots, but there are two complex roots.

We can see this if we solve the equation.

x

2

+

x

+

1

=

0

x

=

−

b

±

√

b

2

−

4

a

c

2

a

=

−

1

±

√

1

2

−

4

×

1

×

1

2

×

1

=

−

1

±

√

1

−

4

2

=

−

1

±

√

−

3

2

=

1

2

(

−

1

±

i

√

3

)

=

−

1

2

(

1

±

i

√

3

)

x

=

—

1

2

(

1

+

i

√

3

)

and

x

=

−

1

2

(

1

−

i

√

3

)

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