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Explain why the equation has imaginary roots when b^2 - 4ac < 0.

User Tanka
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Final answer:

The quadratic equation yields imaginary roots when the discriminant, b² - 4ac, is negative because the square root of a negative number is not real, resulting in complex roots with an imaginary component.

Step-by-step explanation:

The equation ax²+bx+c = 0 is a quadratic equation, and its roots are determined by the quadratic formula -b ± √(b² - 4ac) over 2a. When the discriminant, b² - 4ac, is less than zero, the square root of a negative number results in imaginary roots. Imaginary numbers are not on the real number line and have a component with i, which represents the square root of -1. Therefore, if b² - 4ac < 0, the root of the quadratic equation will include imaginary numbers, leading to two complex roots that are conjugates of each other.

User Dirk
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