How Do You Use the Square Root Method to Solve a Quadratic Equation with Imaginary Solutions if a≠1?

How Do You Use the Square Root Method to Solve a Quadratic Equation with Imaginary Solutions if a≠1?

Note:

The solution to a quadratic equation can sometimes be an imaginary number! This tutorial shows you how to use the square root method to solve a quadratic equation that has imaginary solutions.

Keywords:

  • problem
  • solve
  • solving
  • quadratic equation
  • imaginary solutions
  • solution
  • square root of a negative
  • square root method

Background Tutorials

  • Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

      • What's the Subtraction Property of Equality?What's the Subtraction Property of Equality?

      What's the Subtraction Property of Equality?

      Solving equations can be tough, especially if you've forgotten or have trouble understanding the tools at your disposal. One of those tools is the subtraction property of equality, and it lets you subtract the same number from both sides of an equation. Watch the video to see it in action!

      • What's the Division Property of Equality?What's the Division Property of Equality?

      What's the Division Property of Equality?

      Solving equations can be tough, especially if you've forgotten or have trouble understanding the tools at your disposal. One of those tools is the division property of equality, and it lets you divide both sides of an equation by the same number. Watch the video to see it in action!

  • Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

      • How Do You Simplify the Square Root of a Negative Number?How Do You Simplify the Square Root of a Negative Number?

      How Do You Simplify the Square Root of a Negative Number?

      Simplifying the square root of a negative number is very similar to simplifying the square root of a positive number. You just need to remember 'i' in your answer! Check out this tutorial to see how to simplify the square root of a negative number.

  • Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)^2= q that has the same solutions. Derive the quadratic formula from this form.

      • What is a Quadratic Equation?What is a Quadratic Equation?

      What is a Quadratic Equation?

      You can't go through algebra without seeing quadratic equations. The graphs of quadratic equations are parabolas; they tend to look like a smile or a frown. There's also a bunch of ways to solve these equations! Watch this tutorial and get introduced to quadratic equations!

Further Exploration

  • Solve quadratic equations with real coefficients that have complex solutions.

  • Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.