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The Discriminant. The "stuff" under the square root is called the discriminant . This "discriminates" or tells us what type of solutions we'll have.
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The "stuff" under the square root is called the discriminant. This "discriminates" or tells us what type of solutions we'll have. If we have a quadratic equation and are considering solutions. It is sometimes enough to know what type of number solution it will be. Using the quadratic formula, one of three things can happen. • The "stuff" under the square root can be positive and we'd get Two different real-number solutions. Solutions are rational. Solutions are irrational conjugates
Example Solving 6x² +5x +1 = 0 gives the solutions -⅓, and -½ Solving x² +4x +2 = 0 gives the solutions -2 + √2 and -2 - √2
The "stuff" under the square root can be negative and we'd get Two complex solutions that are conjugates of each other. Example Solving x² + 4x + 5 = 0 gives the solutions -2 + i and 2 – i.
The "stuff" under the square root can be zero and we'd get One solution (called a repeated or double root because it would factor into two equal factors, each giving us the same solution). Example: When b² -4ac simplifies to 0, it doesn’t matter if we use + √b²-4ac or -√b² -4ac; we get the same solution twice. Thus, when the discriminant is 0, there is one repeated solution and it is rational Solving 9x² + 6x + 1 = 0 gives the (repeated) solution -⅓.
