Question

When the solution are going to be complex.

Which methods can be used to solve quadratic equations?

Answer 1

Step-1: Explanation :

The discriminant for the quadratic equation $a{x}^2+bx+c=0$ can be given as follows:

$△=b^2-4ac$

When this value of discriminant is less than zero the quadratic equation is said to have complex roots.

Step-2: Find the methods use to solve quadratic equation

We use quadratic formula to find the roots of the quadratic equation,.

Consider a quadratic equation $x^2-4x+5=0$

The determinant of the above equation can be given as follows:

$$\begin{gathered} △=\sqrt{4^2-4\left(1\right)\left(4\right)} \\ △=\sqrt{16-20} \\ △=\sqrt{-4} \\ △=2i \end{gathered}$$

As the value of the discriminant is less than zero the equation has imaginary roots

Now use quadratic formula to find the roots of the equation

The quadratic formula can be given as follows:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Substituting the value in the equation and solving it we get,

$$\begin{gathered} x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ x=\frac{4\pm 2i}{2} \\ x=2\pm i \end{gathered}$$\

Therefore, the quadratic equation is said to have complex roots it the value of discriminant is less than zero.

Also we can solve a quadratic equation by using the quadratic formula.