Understanding the Nature of Roots: Explaining the Significance of the Discriminant in Quadratic Equations

If b²-4ac > 0

If the expression b²-4ac is greater than 0, it means that the discriminant of a quadratic equation is positive

If the expression b²-4ac is greater than 0, it means that the discriminant of a quadratic equation is positive. The discriminant is a term used to determine the nature of the roots of a quadratic equation. The quadratic equation is in the form of ax² + bx + c = 0, where a, b, and c are coefficients.

When the discriminant is greater than 0, it indicates that the quadratic equation has two distinct real roots. These roots can be found using the quadratic formula: x = (-b ± √(b²-4ac)) / (2a).

For example, let’s say we have the quadratic equation 2x² + 5x – 3 = 0. We can calculate the discriminant using the formula b²-4ac:

Discriminant = (5)² – 4(2)(-3)
= 25 + 24
= 49

Since the discriminant (49) is greater than 0, it tells us that this quadratic equation has two distinct real roots. We can now use the quadratic formula to find the values of x:

x = (-5 ± √(49)) / (2*2)
= (-5 ± 7) / 4

This means that the roots of the equation 2x² + 5x – 3 = 0 are x = -3/2 and x = 1/2.

In summary, when the expression b²-4ac is greater than 0, it indicates that the quadratic equation has two distinct real roots.

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