determine the nature of the roots of xx+3x+6=0

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Asked 3/8/2010 5:32:46 AM

Updated 328 days ago|7/21/2023 12:52:11 AM

1 Answer/Comment

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Question

Asked 3/8/2010 5:32:46 AM

Updated 328 days ago|7/21/2023 12:52:11 AM

1 Answer/Comment

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3

The nature of the roots of x^2 + 3x + 6 = 0 is complex (imaginary) roots.

Added 328 days ago|7/21/2023 12:51:47 AM

This answer has been confirmed as correct and helpful.

3

Examine the discriminant (b^2 - 4ac) of the equation.

In this case, a = 1, b = 3, and c = 6.

The discriminant is calculated as follows:

Discriminant = (3^2) - 4(1)(6)

= 9 - 24

= -15

Since the discriminant (-15) is negative, the quadratic equation has complex roots. Specifically, it has two imaginary roots, indicating that the equation does not intersect the x-axis and has no real solutions.

Therefore, the nature of the roots of x^2 + 3x + 6 = 0 is complex (imaginary) roots.

In this case, a = 1, b = 3, and c = 6.

The discriminant is calculated as follows:

Discriminant = (3^2) - 4(1)(6)

= 9 - 24

= -15

Since the discriminant (-15) is negative, the quadratic equation has complex roots. Specifically, it has two imaginary roots, indicating that the equation does not intersect the x-axis and has no real solutions.

Therefore, the nature of the roots of x^2 + 3x + 6 = 0 is complex (imaginary) roots.

Added 328 days ago|7/21/2023 12:52:11 AM

This answer has been confirmed as correct and helpful.

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