Question

If the discriminant of a quadratic equation is -8 which statement best 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: Two complex roots (choice A)

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Step-by-step explanation:

Let D be the discriminant of a quadratic.

The general rule is

• If D is a positive number (ie larger than 0), then you have two different real roots.
• If D is equal to 0, then you have exactly one real root
• If D is negative, then you'll have two imaginary or complex roots.

In this case, the discriminant is D = -8. That satisfies D < 0 which is the third case mentioned above.

Answer 2

`\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ y=\stackrel{\stackrel{a}{\downarrow }}{a}x^2\stackrel{\stackrel{b}{\downarrow }}{+b}x\stackrel{\stackrel{c}{\downarrow }}{+c} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution}\\ &\textit{two complex roots} \end{cases}`

bearing in mind that complex (imaginary) roots are never by their lonesome, their sibling sister is always with them.