Question

Using quadratic formula, find the roots of the following equations x^2+6x_10=0​

Answer 1

Explanation:

x

2

+

6

x

+

10

=

0

Comparing with standard quadratic equation

a

x

2

+

b

x

+

c

=

0

a

=

1

,

b

=

6

,

c

=

10

Discriminant

D

=

b

2

−

4

a

c

or

D

=

36

−

40

=

−

4

If discriminant positive, we get two real

solutions, if it is zero we get just one solution, and if it is negative

we get complex solutions. Discriminant is negative , so it has

complex roots. .Quadratic formula:

x

=

−

b

±

√

D

2

a

or

x

=

−

6

±

√

−

4

−

2

=

−

3

±

i

[

i

2

=

−

1

]

So roots are

x

=

−

3

+

1

i

and

x

=

−

3

−

1

i

[Ans]

Answer 2

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By using quadratic formula

$\large \bigstar \: \: \boxed{ \sf x = \frac{ - b\pm \sqrt{ {b}^{2} - 4ac} }{2a}}$

Here

• a = 1
• b = 6
• c = - 10

Substitute values in formula

$\longmapsto \sf x = \frac{ - 6 \pm \sqrt{ {6}^{2} - 4 \times 1 \times ( - 10) } }{2 \times 1}$

$\longmapsto \sf x = \frac{ - 6 \pm \sqrt{36 + 40 } }{2}$

$\longmapsto \sf x = \frac{ - 6 \pm \sqrt{76 } }{2}$

Taking +ve sign

$\longmapsto \sf x = \frac{ - 6 + \sqrt{76 } }{2}$

Taking - ve sign

$\longmapsto \sf x = \frac{ - 6 - \sqrt{76 } }{2}$