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The square of any real number is non-negative. So no real number can have a negative square. Consequently, a negative number cannot have a real square root. If the discriminant is less than zero, the quadratic equation requires the square root of that negative value, which cannot be real and so must be imaginary.

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Q: Explain why the roots of a quadratic equation are imaginary if the value of the discriminant is less than 0?
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