Example 2: Completing the square | Quadratic equations | Algebra I | Khan Academy

TL;DR

This video explains how to find the roots of a quadratic equation using the completing the square method.

Transcript

Use completing the square to find the roots of the quadratic equation right here. And when anyone talks about roots, this just means find the x's where y is equal to 0. That's what a root is. A root is an x value that will make this quadratic function equal 0, that will make y equal 0. So to find the x's, let's just make y equal 0 and then solve fo... Read More

Key Insights

• 🟰 The process of finding the roots of a quadratic equation involves making y equal to 0 and solving for x.
• ❎ Completing the square allows us to turn a quadratic equation into a perfect square trinomial.
• 🫚 Not all quadratic equations have real roots; some may only have complex roots.
• 🤑 The completing the square method can be used to solve quadratic equations with any coefficients, even ones with decimal values.
• ❎ Taking the square root of a negative number is not possible when dealing with real numbers.
• ☺️ The fact that the equation cannot be solved for real values of x indicates that there are no real roots.
• 🫚 Factoring may not always be a feasible method for finding the roots of a quadratic equation.

Questions & Answers

Q: What does it mean to find the roots of a quadratic equation?

Finding the roots of a quadratic equation refers to finding the values of x that make the equation equal to zero.

Q: How do you turn a quadratic equation into a perfect square trinomial using completing the square?

To turn a quadratic equation into a perfect square trinomial, you can add and subtract half of the coefficient of the x term, squared, to complete the square.

Q: Can the completing the square method be used for all quadratic equations?

Yes, the completing the square method can be used for all quadratic equations, regardless of whether they are factorable or not.

Q: What does it mean if there are no real roots to a quadratic equation?

If there are no real roots to a quadratic equation, it means that there are no real values of x that satisfy the equation and make it equal to zero.

Summary & Key Takeaways

• The video demonstrates the process of finding the roots of a quadratic equation by making y equal to 0 and solving for x.

• Completing the square is used to turn part of the equation into a perfect square trinomial.

• If it is not possible to find a real number that satisfies the equation, there are no real roots.