If b²-4ac < 0
When we have an expression b²-4ac where the value is less than 0, it means that the discriminant is negative
When we have an expression b²-4ac where the value is less than 0, it means that the discriminant is negative. This situation occurs when solving quadratic equations, specifically when using the quadratic formula.
The quadratic formula is used to find the roots, or solutions, of a quadratic equation of the form ax²+bx+c=0. To determine if the equation has real solutions, we look at the value of b²-4ac, which is called the discriminant.
If the discriminant is negative (b²-4ac < 0), it means that the quadratic equation has no real solutions. In other words, the equation does not intersect the x-axis and does not have any real roots. The graph of the equation will either be entirely above or below the x-axis, depending on the coefficients a, b, and c. For example, let's consider the equation x²+2x+5=0. Here, a=1, b=2, and c=5. To find the discriminant, we substitute these values into the formula: b²-4ac = (2)² - 4(1)(5) = 4 - 20 = -16. Since the discriminant is negative, the quadratic equation x²+2x+5=0 has no real solutions. In summary, if b²-4ac < 0, it means the quadratic equation has no real solutions and the graph of the equation does not intersect the x-axis.
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