Does quadratic formula work with imaginary numbers?

Does quadratic formula work with imaginary numbers?

In relation to quadratic equations, imaginary numbers (and complex numbers) occur when the value under the radical portion of the quadratic formula is negative. When this occurs, the equation has no roots (zeros) in the set of real numbers. These complex roots will be expressed in the form a + bi.

How do you know if a graph has imaginary zeros?

Imaginary roots appear in a quadratic equation when the discriminant of the quadratic equation — the part under the square root sign (b2 – 4ac) — is negative. If this value is negative, you can’t actually take the square root, and the answers are not real.

Why does a quadratic equation Cannot have one imaginary solution?

A quadratic equation may take complex values for x but the coefficients are always real. This makes both b and c complex, which is not allowed as they have to be real. This is the reason why if quadratic equations have complex roots, they are in pairs and form complex conjugates.

Can all quadratic equations be solved by factoring?

No, not all quadratic equations can be solved by factoring. This is because not all quadratic expressions, ax2 + bx + c, are factorable.

Can a quadratic equation have one real solution and one non real solution?

If you get a positive number, the quadratic will have two unique solutions. If you get 0, the quadratic will have exactly one solution, a double root. If you get a negative number, the quadratic will have no real solutions, just two imaginary ones.

What are the steps for solving a quadratic equation?

Steps to solve quadratic equations by factoring: 1. Write the equation in standard form (equal to 0). 2. Factor the polynomial. 3. Use the Zero Product Property to set each factor equal to zero. 4. Solve each resulting linear equation.

What is the correct quadratic formula?

The standard form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are coefficiencts and y and x are variables.

Which method to solve a quadratic equation?

Method 1 of 3: Factoring the Equation. Combine all of the like terms and move them to one side of the equation.

  • Method 2 of 3: Using the Quadratic Formula. Combine all of the like terms and move them to one side of the equation. Write down the quadratic formula.
  • Method 3 of 3: Completing the Square. Move all of the terms to one side of the equation.
  • How do you calculate the quadratic equation?

    A quadratic equation is written as #ax^2+bx+c# in its standard form. And the vertex can be found by using the formula #-b/(2a)#. For example, let’s suppose our problem is to find out vertex (x,y) of the quadratic equation #x^2+2x-3# . 1) Assess your a, b and c values. In this example, a=1, b=2 and c=-3.