How Do You Solve a Quadratic Equation With Complex Solutions by Using the Quadratic Formula?

How Do You Solve a Quadratic Equation With Complex Solutions by Using the Quadratic Formula?

Note:

You can never get too much practice working with the quadratic formula, especially when the solution includes complex numbers! Watch this tutorial to see the quadratic formula be used to find the complex solutions to a quadratic equation.

Keywords:

  • problem
  • solve
  • solving
  • quadratic equation
  • complex solutions
  • solution
  • quadratic formula

Background Tutorials

  • Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

      • How Do You Evaluate an Algebraic Expression?How Do You Evaluate an Algebraic Expression?

      How Do You Evaluate an Algebraic Expression?

      Plugging variables into an expression is essential for solving many algebra problems. See how to plug in variable values by watching this tutorial.

      • What's the Order of Operations?What's the Order of Operations?

      What's the Order of Operations?

      Check out this tutorial where you'll see exactly what order you need to follow when you simplify expressions. You'll also see what happens when you don't follow these rules, and you'll find out why order of operations is so important!

  • Apply the properties of operations to generate equivalent expressions.

  • 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!

      • What is the Quadratic Formula?What is the Quadratic Formula?

      What is the Quadratic Formula?

      If you're solving quadratic equations, knowing the quadratic formula is a MUST! This formula is normally used when no other methods for solving quadratics can be reasonably used. In this tutorial, learn about the quadratic formula and see it used to solve a quadratic equation. Take a look!

  • 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.

      • How Do You Find the a, b, and c Values of a Quadratic Function?How Do You Find the a, b, and c Values of a Quadratic Function?

      How Do You Find the a, b, and c Values of a Quadratic Function?

      When you're dealing with quadratic equations, it can be really helpful to identify a, b, and c. These values are used to find the axis of symmetry, the discriminant, and even the roots using the quadratic formula. It's no question that it's important to know how to identify these values in a quadratic equation. This tutorial shows you how!

Further Exploration

  • 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.

      • How Do You Solve a Quadratic Equation by Using the Quadratic Formula?How Do You Solve a Quadratic Equation by Using the Quadratic Formula?

      How Do You Solve a Quadratic Equation by Using the Quadratic Formula?

      One of the many ways you can solve a quadratic equation is by using the quadratic formula. The quadratic formula is usually chosen when the other methods won't work or are difficult to use. In this tutorial, see how to solve a quadratic equation using the quadratic formula!