Double root
Identify a double root when a quadratic has one repeated solution, meaning the discriminant equals zero. Understand Grade 9 quadratic structure through repeated factors.
Key Concepts
Property If $b^2 4ac = 0$, then there is one real solution, which means there is one x intercept. The solution is called a double root of the equation. Explanation When the discriminant is zero, it’s like the two solutions of a quadratic equation have merged into one! The parabola's vertex sits perfectly on the x axis, giving you one x intercept. It's called a 'double root' because it technically counts as two identical solutions, making it extra special. Examples The equation $x^2 + 8x + 16 = 0$ has a discriminant of $0$, resulting in a double root. The equation $4x^2 12x + 9 = 0$ has a discriminant of $0$, resulting in a double root. The equation $x^2 2x + 1 = 0$ has a discriminant of $0$, resulting in a double root.
Common Questions
What is Double root in Grade 9 algebra?
It is a core concept in Grade 9 algebra that builds problem-solving skills and prepares students for advanced math coursework.
How do you apply double root to solve problems?
Identify the relevant formula or property, substitute known values carefully, apply each step in order, and verify the result makes sense.
What common errors occur with double root?
Misapplying the rule to wrong scenarios, sign mistakes, and forgetting to check answers in the original problem.