Question

atic equations.
x2 + 2x - 9 = 0
solution : Compare it
​

Answer 1

Answer

Shwetank Mauria

Jul 18, 2016

x

=

1

+

i

2

√

2

or

x

=

1

−

i

2

√

2

Step-by-step explanation:

In the equation

x

2

−

2

x

+

9

=

0

, the coefficients are rational but as the discriminant is

(

−

2

)

2

−

4

×

1

×

9

=

4

−

36

=

−

32

is negative, the roots of the equation are pair of complex conjugate numbers. Hence, we can use quadratic formula to get roots.

Quadratic formula gives the roots of

a

x

2

+

b

x

+

c

=

0

as

x

=

−

b

±

√

b

2

−

4

a

c

2

a

. Note that

b

2

−

4

a

c

is the discriminant.

Hence solution of

x

2

−

2

x

+

9

=

0

is given by

x

=

−

(

−

2

)

±

√

(

−

2

)

2

−

4

×

1

×

9

2

×

1

or

x

=

2

±

√

−

32

2

i.e.

x

=

2

+

i

4

√

2

2

or

x

=

2

−

i

4

√

2

2

i.e.

x

=

1

+

i

2

√

2

or

x

=

1

−

i

2

√

2