You didn't expect this "quadratic" equation to have 6 solutions!

TL;DR

Adding absolute value to a quadratic equation can result in six solutions, including real and complex numbers.

Transcript

so we all know that this is a quadratic equation and we can solve this one by factoring and we end up with two solutions so it's not too much fun right so this is what I did I decided to put absolute value around this X and guess what we will end up with six soluions just like Michael Jordan six championships and I was really surprised and I tried ... Read More

Key Insights

• 🪜 Adding absolute value to a quadratic equation can increase the number of solutions.
• ❎ Absolute value can be represented as the square root of the squared value in solving complex numbers.
• 🤘 Considering the signs of the variables is crucial in determining the different cases for the solutions.
• #️⃣ The solutions can be a combination of real and complex numbers.
• 🤩 The key to obtaining six solutions lies in considering both the real and complex parts of the equation.
• 🖐️ Absolute value plays a significant role in measuring distance and solving for complex numbers.
• 💦 Case work is necessary to determine the solutions based on the signs of the variables.

Questions & Answers

Q: How does adding absolute value to a quadratic equation affect the number of solutions?

Adding absolute value to a quadratic equation can increase the number of solutions from two to six, including real and complex numbers.

Q: What is the definition of absolute value and how is it used in solving quadratic equations?

Absolute value measures the distance of a complex number from the origin on a complex plane. It can be represented as the square root of the sum of the squares of the real and imaginary parts. In quadratic equations, absolute value can be used to solve for complex solutions.

Q: What are the different cases that need to be considered when solving for the six solutions?

The different cases involve considering the signs of the variables in the quadratic equation. If the variable is greater than zero, it corresponds to a positive solution. If the variable is less than zero, it corresponds to a negative solution. And if the variable is zero, it corresponds to a purely imaginary solution.

Q: Can you explain how the six solutions are obtained in detail?

The six solutions are obtained by considering different cases for the signs of the variables. When the variable is greater than zero, it results in two real solutions (positive and negative). When the variable is zero, it results in two purely imaginary solutions (positive and negative). And when the variable is less than zero, it results in two real solutions (positive and negative).

Summary & Key Takeaways

• By adding absolute value to a quadratic equation, the number of solutions increases from two to six.

• Absolute value can be represented as the square root of the squared value, which is helpful in solving complex numbers.

• By considering different cases based on the signs of the variables, the six solutions can be determined.