If the quadratic has a positive coefficient of 𝑥 2 (a > 0), the graph is concave up and the minimum point will touch 𝑥-axis as shown in the left image below. Instead it just touches it at its one root. This means that the graph of the quadratic just touches the 𝑥-axis at its minimum or maximum point.Ī discriminant equal to zero means that the graph of the quadratic equation must touch the 𝑥-axis once. A quadratic equation with a discriminant of zero has exactly one solution. A Discriminant of ZeroĪ discriminant of zero means that the value of b 2 – 4ac is equal to zero. This is because the square root of this discriminant will be a surd. If a discriminant is not a perfect square, the 2 solutions will be irrational. This means that the solutions will be integers or can be written as fractions. If the discriminant is a perfect square, then the solutions to the quadratic equation are rational. Therefore the quadratic formula provides 2 different solutions. In some books, the discriminant is represented by the greek letter (delta), and b 2 4ac. The square root of a positive number has both a positive and negative answer. The discriminant of the quadratic equation is the part that is below the square root of the quadratic formula. When we subtract a negative number, an addition takes place.
When we square a negative number, it gives us a positive result. When calculating the discriminant it is important to consider these key points: Substitute the values of a, b and c after reading them from a quadratic equation of the form a𝑥 2 + b𝑥 + c. To calculate the discriminant of a quadratic equation, the formula is b 2 – 4ac. The following table shows the number of roots for a positive, negative or zero discriminant. The roots of a quadratic equation are the locations where the quadratic graph crosses the 𝑥-axis. The number of solutions to a quadratic equation tells us the number of roots of the quadratic equation.
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