Understanding the Significance of b²-4ac = 0 in Quadratic Equations: Exploring the Nature of Roots

If b²-4ac = 0

If b²-4ac = 0 in a quadratic equation of the form ax² + bx + c = 0, it means that the discriminant, which is the expression b² – 4ac, is equal to zero

If b²-4ac = 0 in a quadratic equation of the form ax² + bx + c = 0, it means that the discriminant, which is the expression b² – 4ac, is equal to zero.

The discriminant is used to determine the nature of the roots of a quadratic equation. When the discriminant is zero, it indicates that the quadratic equation has two identical real roots.

To understand this further, let’s break down the equation b²-4ac = 0:

– If the discriminant is positive (b²-4ac > 0), it indicates that there are two distinct real roots.
– If the discriminant is zero (b²-4ac = 0), it means that there is only one real root, and it is repeated or has a multiplicity of 2.
– If the discriminant is negative (b²-4ac < 0), it shows that the quadratic equation has no real roots. In this case, the equation would have complex roots. For example, let's say we have the quadratic equation 2x² + 4x + 2 = 0. Here, a = 2, b = 4, and c = 2. Calculating the discriminant: b² - 4ac = 4² - 4(2)(2) = 16 - 16 = 0. Since the discriminant is zero, we know that the equation has only one real root. In this case, that real root is x = -1. So, if b² - 4ac = 0, it means that the quadratic equation has exactly one real root with a multiplicity of 2.

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