If b²-4ac > 0
There are 2 real roots
The expression b²-4ac represents the discriminant of a quadratic equation in the standard form ax²+bx+c=0.
When b²-4ac is greater than 0, it means that the discriminant is positive. In other words, there are two distinct real roots that can be found for the quadratic equation.
Geometrically, this means that the parabola represented by the equation intersects the x-axis at two points.
For example, the quadratic equation x²-4x+3=0 has a discriminant of 4-4(1)(3) = 4-12 = -8, which is negative. This means that the equation has no real roots.
On the other hand, the quadratic equation x²-4x-3=0 has a discriminant of 4-4(1)(-3) = 16, which is positive. This means that the equation has two real roots. By using the quadratic formula, we can find the roots as follows:
x = (-b ± √(b²-4ac))/2a
x = (4 ± √16+12)/2
x = (4 ± √28)/2
x ≈ 0.56 or x ≈ 3.44.
Therefore, when the discriminant is positive, the quadratic equation has two real roots that can be found using the quadratic formula.
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