Another common type of a quadratic equation is a quadratic equation without any constant. That is, each equation

^{2}+ bx = 0 where a, b ∈ ℝ and a≠0.

is a quadratic equation without constant. The approach how to find roots of such equation is easy. Let’s take an example

^{2}− 4x = 0.

We can factor out the variable *x*:

8x^{2} − 4x | = | 0 |

x · (8x − 4) | = | 0 |

We can immediately see one of the roots: it’s the *x _{1} = 0*. Because if we substitute

*x*for zero, the equation definitely holds since

Ok, now the expression inside parenthesis. The whole left part of the equation equals zero when the inside of the parenthesis equals zero. Thus we’re actually solving linear equation *8x − 4 = 0*. We can find the root of this equation easily

The second root is *x _{2} = ½*. Let’s take a look at the graph:

The graph of quadratic function *f(x) = 8x ^{2} − 4x* intersects the horizontal axis in two points:

*(0, 0)*and

*(½, 0)*. It’s exactly what we’ve solved.