Question

If the discriminant of a quadratic equation is equal to Negative 8, which statement describes the roots?
There are two complex roots.
There are two real roots.
There is one real root.
There is one complex root.

Answer 1

Answer:

A. There are two complex roots

Step-by-step explanation:

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Answer 2

If the discriminant of a quadratic equation is equal to Negative 8, there are two complex roots.

Discriminant of quadratic equation

The discriminant of a quadratic equation is given as;

$b^2 - 4ac>0 \ \ ( 2 \ solutions; 1 \ positive \ and \ 1 \ negative\ solution)\\\\b^2 -4ac = 0 \ \ (1 \ real \ solution)\\\\b^2 - 4ac \ < 0 \ \ (complex \ root, \ no \ solution)$

A discriminant of negative 8 falls with last category in the solution above.

$b^2 - 4ac <0 \ \ (eg \ -8),$

$x = +/-\sqrt{-8} \\\\x = \sqrt{-8 } \ \ or \ \ -\sqrt{-8} \ \ \ \ \ (2 \ complex \ roots)$

Thus, if the discriminant of a quadratic equation is equal to Negative 8, there are two complex roots.

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