Question

if the roots of the quadratic equation are complex, then ______.

\\(\delta < 0\\)

\\(\delta = 0\\)

Explanation:

Define the discriminant of a quadratic equation

The discriminant of a quadratic equation \(ax^2 + bx + c = 0\) is denoted by \(\Delta\) (or \(D\)) and is given by:

$$ \Delta = b^2 - 4ac $$

Determine the condition for complex roots

The nature of the roots depends on the sign of the discriminant \(\Delta\):

• If \(\Delta > 0\), the equation has two distinct real roots.
• If \(\Delta = 0\), the equation has one repeated real root.
• If \(\Delta < 0\), the equation has two complex (conjugate) roots.

Answer:

• \(\Delta < 0\) (Correct answer)
• \(\Delta = 0\)