The Quadratic Equation: How A Negative Discriminant Leads To Complex Roots

If b²-4ac < 0

There are no roots

If b²-4ac is less than zero, then the quadratic expression ax²+bx+c will have no real roots. This is because the value of the discriminant, b²-4ac, is used to determine the nature of the roots of the quadratic equation.

When the value of b²-4ac is less than zero, it implies that the expression under the square root is negative. Since the square root of a negative number doesn’t have any real solution, the quadratic equation cannot have any real roots. In such a situation, the equation will only have complex roots, which consists of a real part and an imaginary part.

Geometrically, this means that the graph of the quadratic equation will never intersect the x-axis and will always remain above or below it, depending on the value of the coefficient a.

In summary, if b²-4ac is less than zero, then the quadratic equation ax²+bx+c will have no real roots, only complex roots with a real and imaginary part.

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